Speckle filtering is an indispensable pre-processing step for applications of polarimetric synthetic aperture radar (POLSAR), such as terrain classification, target detection, etc. As one of the most typical methods, the polarimetric whitening filter (PWF) can be used to produce a minimum-speckle image by combining the complex elements of the scattering matrix, but polarimetric information is lost after the filtering process. A polarimetric filter based on subspace decomposition which was proposed by Gu et al specializes in retrieving principle scattering characteristics, but the corresponding mean value of an image after filtering is not kept well. A new filter is proposed for improving the disadvantage based on subspace decomposition. Under the constraint that a weighted combination of the polarimetric SAR images equals to the output of the PWF, the Euclidean distance between an unfiltered parameter vector and a signal space vector is minimized so that noises can be reduced. It is also shown that the proposed method is equivalent to the subspace filter in the case of no constraint. Experimental results with the NASA/JPL airborne polarimetric SAR data demonstrate the effectiveness of the proposed method.