Online Etymology Dictionary

unharness (v.): mid-15c., "divest of armor," from un- (2) + harness (v.). Cf. Dutch ontharnassen "to disarm." Meaning "to free (a horse) from harness" is recorded from 1610s. Related: Unharnessed; unharnessing.
unhealthy (adj.): 1590s, "injurious to health," from un- (1) "not" + healthy. Earlier unhealthsome (1540s), unhealthful (1570s). Of persons, "sickly," it is attested from 1610s. Related: Unhealthily.
unheard (adj.): c.1300 "not detected by sense of hearing," from un- (1) "not" + past participle of hear. Meaning "unknown, new" is attested from late 14c. (Old English had ungehered in this sense). Usually with of since 1590s. Cf. Old Norse oheyrðr, Danish uhørt, Middle Dutch ongehoort, Old High German ungehoret.
unheeded (adj.): 1610s, from un- (1) "not" + past participle of heed.
unhelpful (adj.): 1590s, from un- (1) "not" + helpful. Related: Unhelpfully; unhelpfulness.
unheralded (adj.): 1845, from un- (1) "not" + past participle of herald (v.).
unhindered (adj.): 1610s, from un- (1) "not" + past participle of hinder.
unhinge (v.): recorded earlier in the mental sense of "to disorder" the mind, etc. (1612) than in the literal one of "to take (a door, etc.) off its hinges" (1616); from un- (2) + hinge (v.). Related: Unhinged; unhinging.
unhinged (adj.): "thrown into confusion," 1719, past participle adjective from unhinge.
unhitch (v.): 1620s, from un- (2) + hitch (v.). Related: Unhitched; unhitching.
unholy (adj.): Old English unhalig, "impious, profane, wicked," from un- (1) "not" + halig (see holy). Cf. Middle Dutch onheilich, Old Norse uheilagr, Danish unhellig, Swedish ohelig. In reference to actions, it is attested from late 14c. Colloquial sense of "awful, dreadful" is recorded from 1842.
unhorse (v.): late 14c., "to throw (someone) from his horse," from un- (2) + horse (v.). Cf. Middle Dutch ontorsen.
unhuman (adj.): 1540s, "inhumane, cruel," from un- (1) "not" + human. Meaning "superhuman" is from 1782.
unhygienic (adj.): 1883, from un- (1) "not" + hygenic.
uni-: word-forming element meaning "having one only," from Latin uni-, comb. form of unus (see one).
Uniate: "pertaining to an Eastern Christian church that acknowledges the supremacy of the Pope," 1833, from Russian uniyat, from unia "unity, union," from Latin unus "one" (see one).
unicameral (adj.): 1853, from uni- "one" + Late Latin camera "chamber" (see camera).
UNICEF: by 1948, acronym from United Nations International Children's Emergency Fund, which was created in 1946 (the name was changed 1953 to United Nations Children's Fund but the acronym endured).
unicellular (adj.): 1858; see uni- + cellular.
unicorn (n.): early 13c., from Old French unicorne, from Late Latin unicornus (Vulgate), from noun use of Latin unicornis (adj.) "having one horn," from uni- "one" (see uni-) + cornus "horn" (see horn).

The Late Latin word translates Greek monoceros, itself rendering Hebrew re'em, which was probably a kind of wild ox. According to Pliny, a creature with a horse's body, deer's head, elephant's feet, lion's tail, and one black horn two cubits long projecting from its forehead. Cf. German Einhorn, Welsh ungorn, Breton uncorn, Old Church Slavonic ino-rogu.
unicycle (n.): 1869, American English, from Latin uni- "one" (see uni-) + -cycle, from bicycle (from Greek kyklos "circle, wheel").
unidentifiable (adj.): 1859, from un- + identifiable.
unidentified (adj.): 1860, from un- (1) "not" + past participle of identify.
unidirectional (adj.): 1883, from uni- + directional (see direction).
unification (n.): 1851, noun of action from unify. Unification Church was founded 1954.
uniform (adj.): 1530s, "of one form," from Middle French uniforme (14c.), from Latin uniformis "having one form," from uni- "one" (see uni-) + forma "form" (see form). Related: Uniformly.
uniform (n.): "distinctive clothes worn by one group," 1748, from French uniforme, from the adjective (see uniform (adj.)).
uniformity (n.): early 15c., from Old French uniformite (14c.), from Late Latin uniformitatem (nominative uniformitas), from Latin uniformis (see uniform (adj.)).
unify (v.): c.1500, "to make into one," from Middle French unifier (14c.), from Late Latin unificare "make one," from Latin uni- "one" (see uni-) + root of facere "to make" (see factitious). Related: Unified; unifying. Unified (field) theory in physics is recorded from 1935.
unilateral (adj.): 1802, from Modern Latin unilateralis, from unum, neuter of unus "one" (see one) + latus (genitive lateralis) "side" (see oblate (n.)). Jeremy Bentham (1748-1832) may have been the first to use it in the legal sense of "made or entered into by one party." Unilateral disarmament is recorded from 1929.
It is useless for the sheep to pass resolutions in favor of vegetarianism, while the wolf remains of a different opinion. [William Ralph Inge, "Outspoken Essays," 1919]
unilateralism (n.): 1926, from unilateral + -ism. Earliest usages seem to be in the sense of "advocate of unilateral disarmament." Meaning "pursuit of a foreign policy without allies" is attested by 1964.
unimaginable (adj.): 1610s, from un- (1) "not" + imaginable. Related: Unimaginably.
unimpaired (adj.): 1580s, from un- (1) "not" + past participle of impair. Rare before c.1760.
unimpeachable (adj.): 1784, from un- (1) "not" + impeachable. Related: Unimpeachably.
unimpeded (adj.): 1760, from un- (1) "not" + past participle of impede.
unimportant (adj.): 1750, from un- (1) "not" + important. Used earlier in a sense of "unassuming, modest" (1727). Related: Unimportantly.
unimpressed (adj.): 1861, "not awed," from un- (1) "not" + past participle of impress. Used earlier in a sense of "not subjected to restraint" (1743). Unimpressive is recorded from 1796.
unimproved (adj.): 1660s, "not made better," from un- (1) "not" + past participle of improve. Sense of "not developed or taken advantage of" (of land) is recorded from 1781.
unincorporated (adj.): 1715, from un- (1) "not" + past participle of incorporate.
uninflected (adj.): 1713, from un- (1) "not" + past participle of inflect.
uninformed (adj.): 1590s, from un- (1) "not" + past participle of inform. Originally in reference to some specific matter or subject; general sense of "uneducated, ignorant" is recorded from 1640s.
uninhabitable (adj.): mid-15c., from un- (1) "not" + inhabitable.
uninhabited (adj.): 1570s, from un- (1) "not" + past participle of inhabit (v.).
uninhibited (adj.): 1880, from un- (1) "not" + past participle of inhibit.
uninitiated (adj.): 1670s, from un- (1) "not" + past participle of initiate (v.).
unintelligent (adj.): c.1600, from un- (1) "not" + intelligent. Related: Unintelligently.
unintelligible (adj.): 1610s, "incapable of being understood," from un- (1) "not" + intelligible. Related: Unintelligibly.
unintended (adj.): 1640s, from un- (1) "not" + past participle of intend.
unintentional (adj.): 1782, from un- (1) "not" + intentional. Related: Unintentionally (1769).
uninterested (adj.): 1640s, "unbiased," from un- (1) "not" + past participle of interest. It later meant "disinterested" (1660s); sense of "unconcerned, indifferent" is recorded from 1771. This is the correct word for what often is miscalled disinterested.