Although fingerprint recognition is a mature technology and nowadays commercial state-of-the-art systems can be successfully used in a number of real applications, not all the problems have been solved and the research is still very active in the field. This paper presents a new approach for estimating the shift and rotation parameters between fingerprint images stored in the dadabase that operates in the third-order frequency-domain measure called the auto-bispectrum, which, allows us to estimate the shift and the rotation separately. The diagonal slices and their spectra of auto- and cross-bispectrum are proposed. The rotation parameters are estimated from the remaining polar sampled the third-order spectrum using cross-correlation, and then, after compensating for rotation, we may easily estimate the translational component, e.g., by using phase correlation.Experimental evidence of this performance is presented, and the mathematical reasons behind these characteristics are explained in depth. We compare our approach in a simulation to other frequency-domain fingerprint recognition algorithms. We find that our algorithm can better estimate shift and rotation parameters than the other methods.