Source : Webster's Revised Unabridged Dictionary (1913)

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

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

Source : WordNet®

unaccountably
     adv : in an unaccountable manner; "in the book, a tycoon
           unaccountably becomes the hero's friend"