The paper shows a moving least squares reconstruction technique applied to the B-spline Material Point Method (B-spline MPM). It has been shown previously that B-spline MPM can reduce grid-crossing errors inherent in the original Material Point Method. However, in the large deformation regime where the gridcrossing occurs more frequently, the convergence rate of B-spline MPMis lower. In this paper, moving least squares reconstruction is employed to retrieve the expected convergence rate. The proposed improvement is examined in terms of the spatial convergence using the methods of manufactured solutions for large deformations.@en