This paper presents a coherent decomposition scheme for polarimetric SAR data. Coherent decomposition means the decomposition is applied to a single or a few scattering matrix data. Based on the scattering matrix acquired with an FM-CW polarimetric SAR system, we have devised a simple decomposition technique using the coherency matrix for the purpose of identifying scatterers. This paper presents the decomposition technique and some decomposition results obtained by a fully polarimetric FM-CW radar. It is shown the scattering mechanisms are well recovered and the orientation angles of wire scatterer are precisely measured.