A problem of restoration of a blurred image obtained by a horizontally rotating camera is considered in this paper. The mathematical model of this problem is the convolution equation on a cyclic group. In the previous papers of the authors, the case of a non-singular equation was considered. The general case that admits the degeneracy of the convolution equation is considered in this paper. An algorithm is developed based on which a fast program for recovering blurred images is written. The complexity of the algorithm presented in this paper for the degenerate convolution equation is the same as for the non-singular case. The analysis of calculation errors affecting the image quality is given. The influence of the errors of the algorithm's initial data for a degenerate equation is not higher than for a non-singular case.