The paper presents a fingerprint registration approach based on the decomposition of registration process into elementary stages. In each stage a single transformation parameter is eliminated. The algorithm uses composite features, i.e., lines connecting two minutiae instead of fingerprint minutiae. These features have rotation and translation-invariant attributes allowing feature filtering with significantly enhanced signal-to-noise ratio in feature consensus scheme. Experimental results of goal-directed performance evaluation with live-captured fingerprint image database are presented.