Is a truly marginal perturbation of the Gk × Gk WZNW model at k = −2cV(G) an exception to the rule?

It is shown that there exists a truly marginal deformation of the direct sum of two Gk WZNW models at k = −2cV(G) (where cV(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 lagrangians describing the WZNW model is constructed.