We propose a new POLSAR model-based decomposition with a generalized scattering model. The generalized scattering model is built by adding the ellipticity angle with the particle cloud model. The model is flexible so that it represents surface scattering, double-bounce, volume scattering, and helix scattering. Moreover, a decomposition procedure to use the generalized model is proposed. First, the model parameters are determined so that the resultant model matrix can be subtracted from the observed coherency matrix as much as possible with keeping the residual matrix positive semidefinite. Next, the same operation is applied to the residual matrix with a new parameter set. By repeating this process, the residual matrix becomes null at last and the decomposed matrices perfectly fit the observed one. The decomposition results were compared to the results of the eigenvalue-based decomposition. Due to the orientation randomness, the proposed decomposition makes the interpretation straightforward and has a possibility of making the classification easy.