The Collaborative International Dictionary of English v.0.48:

Uncoil \Un*coil"\, v. t. [1st pref. un- + coil.]
   To unwind or open, as a coil of rope. --Derham.
   [1913 Webster]

WordNet (r) 3.0 (2006):

uncoil
    v 1: unwind or untwist [ant: coil, curl, loop]

Moby Thesaurus II by Grady Ward, 1.0:

25 Moby Thesaurus words for "uncoil":
   clarify, clear up, disembroil, disentangle, disintricate,
   disinvolve, ravel, sort out, unbraid, unclutter, unfold, unfurl,
   unknot, unmix, unravel, unreel, unroll, unscramble, unsnarl,
   untangle, unthread, untwine, untwist, unweave, unwind