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In this study, in order to realize the direction selectivity and shift invariability in all analysis levels simultaneously, we propose a method named the 2-dimensional complex discrete wavelet transform (CDWT) by using the RI-spline wavelet. We applied this method in fingerprint analysis. The results obtained can be summarized as follows: (1) The direction selectivity was realized by calculating the sum or difference between wavelet; coefficients that were obtained by the 2D CDWT. (2) 2D CDWT by RI-spline wavelet has been applied to the analysis of a fingerprint, and the direction of the 2D edges in all analysis levels could be extracted alternatively.