It is known that if F is a free group and R is a normal subgroup such that F/R is an infinite group, then the Schur multiplier of F/γc(R) is not finitely generated for all c>1. It is an interesting question, if R, S are two normal subgroups of the free group F, when F/[R, S] is finitely presented, and when is its Schur multiplier finitely generated. We show for most cases (including the cases already known) that if F/RS is infinite then the Schur multiplier of F/[R, S] is not finitely generated. We believe this is true in general. On the other hand if R, S are normally finitely generated and RS is of finite index, then F/[R, S] is finitely presented.