This technical note has twofold aspects. The first aspect is to present some new results on characterization of matrix paracontraction and the second aspect is to correct some errors in the author's previous publication by means of these newly developed results for paracontraction. Specifically, new necessary and/or sufficient conditions to characterize paracontracting matrices using discrete-time semistability, singular value decomposition, normal matrices, and range symmetric matrices are provided. Using these results, one can rectify an error in the author's previous publication.