Is a truly marginal perturbation of the G_ktimes G_k WZNW model at k=-2c_V(G) an exception to the rule?

It is shown that there exists a truly marginal deformation of the direct sum of two $G_k$ WZNW models at $k=-2c_V(G)$ (where $c_V(G)$ is the eigenvalue of the quadratic Casimir operator in the adjoint representation of the group $G$) which does not seem to fit the Chaudhuri-Schwartz criterion for truly marginal perturbations. In addition, a continuous family of WZNW models is constructed.