EN
By means of exact diagonalization we consider the groundstate of the J_{1}-J_{2} spin 1/2 Heisenberg model with an anisotropic interaction term of Dzyaloshinskii-Moriya type. We find that a Dzyaloshinskii-Moriya interaction may create a weak ferromagnetic moment. The interplay between the quantum nature of the groundstate of the pure J_{1}-J_{2} model and the anisotropic Dzyaloshinskii-Moriya interaction favour energetically a well-defined direction of spin alignment creating anisotropic correlations.