Source : Webster's Revised Unabridged Dictionary (1913)

Contrarily \Con"tra*ri*ly\ (? or ?), adv.
   In a contrary manner; in opposition; on the other side; in
   opposite ways.

Source : WordNet®

contrarily
     adv 1: in a contrary disobedient manner [syn: {perversely}, {contrariwise}]
     2: contrary to expectations; "he didn't stay home; on the
        contrary, he went out with his friends" [syn: {to the
        contrary}, {contrariwise}, {on the contrary}]