From WordNet (r) 2.0 (August 2003) [wn]:
correctly
adv : in a correct manner; "he guessed right" [syn: right,
aright] [ant: incorrectly]
From The Collaborative International Dictionary of English v.0.48 [gcide]:
Correctly \Cor*rect"ly\ (k?r-r?kt"l?), adv.
In a correct manner; exactly; acurately; without fault or
error.
[1913 Webster]