We present a general approach for the decomposition of games described in the Game Description Language (GDL). In the field of General Game Playing, the exploration of games described in GDL can be significantly sped up by the decomposition of the problem in sub-problems analyzed separately. Our program can decompose game descriptions with any number of players while addressing the problem of joint moves. This approach is used to identify perfectly separable sub-games but can also decompose serial games composed of two subgames and games with compound moves while avoiding, unlike previous works, to rely on syntactic elements that can be eliminated by simply rewriting the GDL rules. We tested our program on 40 games, compound or not, and we can decompose 32 of them successfully in less than 5 s.