A new formulation of the MNDIF method is introduced to extract highly accurate eigenvalues of concave acoustic cavities. Since the MNDIF method, which was introduced by the author, can be applicable for only convex acoustic cavities, a new approach of dividing a concave cavity into two convex domains and formulating an algebraic eigenvalue problem is proposed in the paper. A system matrix equation, which gives eigenvalues, is obtained from boundary conditions for each domain and the condition of continuity in the interface between the two domains. The validity and accuracy of the proposed method are shown through example studies.