contrarily

from WordNet (r) 3.0 (2006)

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

from The Collaborative International Dictionary of English v.0.48

Contrarily \Con"tra*ri*ly\ (? or ?), adv.
   In a contrary manner; in opposition; on the other side; in
   opposite ways.
   [1913 Webster]