The new algorithm of approximate Karhunen-Loeve (KL) expansion and its application to the problem of texture analysis is proposed in the present report. The main idea of the algorithm is to substitute the true two-dimensional correlation function of the image ensemble by the approximate correlation function which has a factorable form. The problem of KL basis construction may be solved, and this complete basis can be used for image processing. We have studied the efficiency of the proposed procedure in comparison with the wavelet fast approximate KL algorithm, and an earlier proposed algorithm of the diagonalization of correlation matrix experimental estimation. For the textures with well defined space- translation symmetry in horizontal or vertical direction the proposed algorithm may give the best results, the calculation complexity being quite equal.