Summary: The current paper presents an effective deblocking algorithm for block-based coded images using singularity detection in a wavelet transform. Blocking artifacts appear periodically at block boundaries in block-based coded images. The local maxima of a wavelet transform modulus detect all singularities, including blocking artifacts, from multiscale edges. Accordingly, the current study discriminates between a blocking artifact and an edge by estimating the Lipschitz regularity of the local maxima and removing the wavelet transform modulus of a blocking artifact that has a negative Lipschitz regularity exponent. Experimental results showed that the performance of the proposed algorithm was objectively and subjectively superior.