Local magnetic structures in space environments, in particular, those in the diffusion region such as magnetic nulls or separators, are very difficult to identify by satellite measurements but important for understanding of magnetic reconnection. Multi-spacecraft missions such as Cluster or MMS, however, provide an opportunity to reconstruct the fine structures using vector data of space magnetometers. In this paper, we introduce a method for such a local reconstruction, based on the modified radial basis functions (Andreeva & Tsyganenko, 2016, ), used previously for the global magnetic field modeling. A principal advantage of this method is its freedom from a priori assumptions on the magnetic field topology. The method has been tested on 2(1)/(2) and 3D reconnection geometries and provided a good agreement with preset models. The relative errors of null positions, gamma-line directions, and n-ary sumation -surface normal directions are found to be below 6% even with 20% random errors added to the target magnetic field vectors in reconstruction of 3D separator model geometry. Applications of the method to the field reconstruction based on Cluster measurements are also presented and discussed.