The Collaborative International Dictionary of English v.0.48:

Unaccountable \Un`ac*count"a*ble\, a.
   1. Not accountable or responsible; free from control.
      --South.
      [1913 Webster]

   2. Not to be accounted for; inexplicable; not consonant with
      reason or rule; strange; mysterious.
      [1913 Webster] -- Un`ac*count"a*ble*ness], n. --
      Un`ac*count"a*bly, adv.
      [1913 Webster]
      [1913 Webster]