Fingerprint matching is a common technique for biometric authentication. Solid state sensors allow that fingerprint recognition is used in small sized embedded systems. The size of these sensors makes it necessary to store several impressions of the same fing er. In order to reduce memory requirements and matching time all these images can be fused into one larger image. We present a RANSAC based method to determine a rigid transformation which aligns two fingerprint images using solely minutiae coordinates and minutiae angles. The reliability of the method is demonstrated with experimental results.