  A bi-layer quantum frustrated antiferromagnet is studied using an effective
action approach. The action derived from the microscopical Hamiltonian has the
form of the O(3) non-linear sigma model. It is solved in the mean field
approximation with the ultraviolet cut off chosen to fit numerical results. The
obtained phase diagram displays a decrease in the critical value of interlayer
coupling with increase of in-plane frustration. The critical point for a
single-layer frustrated antiferromagnet (the J1-J2 model) is estimated to be
J_{2c} = 0.19 J_1.
