The main goal of this research was to propose a new method of polarimetric SAR data decomposition that will extract additional polarimetric information from the Synthetic Aperture Radar (SAR) images compared to other existing decomposition methods. Most of the current decomposition methods are based on scattering, covariance or coherence matrices describing the radar wave-scattering phenomenon represented in a single pixel of an SAR image. A lot of different decomposition methods have been proposed up to now, but the problem is still open since it has no unique solution. In this research, a new polarimetric decomposition method is proposed that is based on polarimetric signature matrices. Such matrices may be used to reveal hidden information about the image target. Since polarimetric signatures (size 18 × 9) are much larger than scattering (size 2 × 2), covariance (size 3 × 3 or 4 × 4) or coherence (size 3 × 3 or 4 × 4) matrices, it was essential to use appropriate computational tools to calculate the results of the proposed decomposition method within an acceptable time frame. In order to estimate the effectiveness of the presented method, the obtained results were compared with the outcomes of another method of decomposition (Arii decomposition). The conducted research showed that the proposed solution, compared with Arii decomposition, does not overestimate the volume-scattering component in built-up areas and clearly separates objects within the mixed-up areas, where both building, vegetation and surfaces occur.