Built-in functions on the LHS won’t pattern-match

I have this pattern-matching problem:

F(X_,myminus(X_)):=0

F(1,myminus(1))

Works.

G(X_,-X_):=0

G(1,-1)

Oops. (Doesn’t match with Minus either.)

I simply use

H(X_,Y_)):=0/;X==-Y

H(1,-1)

which also leaves no question about

H(-1,1)

but there sure must be a way to use only one LHS variable and this would speed up the pattern matching (uhm, does it really)?