Abstract: Let G=G(A,M,N,B) be a generalized matrix algebra, and a:G→G be a map (without the assumption of additivity). Using the  method of algebraic decomposition, we proved that if  a(XY)=a(X)Y+Xa(Y) held for any X,Y∈G and  at least one of X  and Y was idempotent, then a was an additive derivation on G.

Key words: local derivable map, derivation, generalized matrix algebra