The Collaborative International Dictionary of English v.0.48:

Unweave \Un*weave"\, v. t. [1st pref. un- + weave.]
   To unfold; to undo; to ravel, as what has been woven.
   [1913 Webster]

WordNet (r) 3.0 (2006):

unweave
    v 1: undo strands that have been woven together [ant:
         interweave, weave]

Moby Thesaurus II by Grady Ward, 1.0:

59 Moby Thesaurus words for "unweave":
   answer, bottom, clarify, clear up, crack, debug, decipher, decode,
   disembroil, disentangle, disintricate, disinvolve, divine, do,
   dope, dope out, explain, fathom, figure out, find out,
   find the answer, find the solution, get, get right, guess,
   guess right, have it, hit it, interpret, make out, open the lock,
   plumb, psych, psych out, puzzle out, ravel, ravel out, resolve,
   riddle, solve, sort out, unbraid, unclutter, uncoil, undo, unknot,
   unlock, unmix, unravel, unriddle, unscramble, unsnarl, untangle,
   unthread, untwine, untwist, unwind, work, work out