The point clouds scanned by a 3D laser scanner may be affine transformed when the size and posture of the objects being scanned are different. This type of problem is common, but few algorithms can solve it. Therefore, this Letter proposes a parallel registration algorithm. The algorithm eliminates the effects of the affine matrix in the point cloud, based on a simple whitening operation. Moreover, it also has strong anti-noise performance. The algorithm proposed in this Letter is not only simple in structure, but also shows excellent effects in practical applications and simulations.