This paper presents a new multiview alignment algorithm that performs both the coarse and fine alignment of unordered sets of range scans. Our algorithm selects quadruples of range scans, which have feature points of their 2D projections in common. These quadruples are then verified using an Iterative Closest Point (ICP) algorithm. The accepted quadruples form incomplete models of an object that can be aligned using isometries of the Principal Component Analysis (PCA) in combination with an ICP algorithm. The output of our method is a set of finely aligned meshes. Our method was applied to range scans of different clusters of objects varying in the type of acquisition system, the number of range scans, the scan resolution, and scan accuracy. Results show that our method is both effective and efficient for the alignment of meshes: it is capable of aligning object meshes with various properties, aligns the majority of meshes without a priori knowledge, and doesn?t require a multiview ICP algorithm to improve the final alignment.