  In this paper we extend Rado-Choquet-Kneser theorem for the mappings with
weak homeomorphic Lipschitz boundary data and Dini's smooth boundary but
without restriction on the convexity of image domain, provided that the
Jacobian satisfies a certain boundary condition. The proof is based on a recent
extension of Rado-Choquet-Kneser theorem by Alessandrini and Nesi \cite{ale}
and it is used the approximation principle.
