This paper is an extension of the author's previous work that dealt with a composite rectangular membrane with an oblique interface. In the present study, a practical method is presented for the free vibration analysis of a composite rectangular membrane with two homogeneous regions, of which the interface consists of two rectilinear parts and is named 'bent interface'. To the author's best knowledge, the vibration analysis of the composite membrane with this configuration is attempted for the first time in the paper. In order to extract the global system matrix of which the determinant gives natural frequencies, a special way of individually considering the two rectilinear parts of the bent interface and extracting local system matrices by means of applying the compatibility condition to each rectilinear part is revised. Case studies show that the natural frequencies and mode shapes obtained by the present method agree well with those given by exact solutions or FEM (ANSYS), even when a small number of base functions are used.