Abstract Non-rigid structure from motion is a fundamental problem in computer vision, which is yet to be solved satisfactorily. The main diffificulty of the problem lies in choosing the right constraints for the solution. In this paper, we propose new constraints that are more effective for non-rigid shape recovery. Unlike the other proposals which have mainly focused on restricting the deformation space using rank constraints, our proposal constrains the motion parameters so that the 3D shapes are most closely aligned to each other, which makes the rank constraints unnecessary. Based on these constraints, we defifine a new class of probability distribution called the Procrustean normal distribution and propose a new NRSfM algorithm, EM-PND. The experimental results show that the proposed method outperforms the existing methods, and it works well even if there is no temporal dependence between the observed samples