In this paper, we present a new algorithm for non-linear registration of point sets. We estimate both forward and backward deformations fields best superposing the two point sets of interest and we make sure that they are consistent with each other by designing a symmetric cost function where they are coupled. Regularisation terms are included in this cost function to enforce deformation smoothness. Then we present a two-step iterative algorithm to optimise this cost function, where the two fields and the fuzzy matches between the two sets are estimated in turn. Building regularisers using the RKHS theory allows to obtain fast and efficient closed-form solutions for the optimal fields. The resulting algorithm is efficient and can deal with large point sets.