Iterative Filtering (IF) is an alternative technique to the Empirical Mode Decomposition (EMD) algorithm for the decomposition of non–stationary and non–linear signals. Recently in  IF has been proved to be convergent for any L
2 signal and its stability has been also demonstrated through examples. Furthermore in  the so called Fokker–Planck (FP) filters have been introduced. They are smooth at every point and have compact supports. Based on those results, in this paper we introduce the Multidimensional Iterative Filtering (MIF) technique for the decomposition and time–frequency analysis of non–stationary high–dimensional signals. We present the extension of FP filters to higher dimensions. We prove convergence results under general sufficient conditions on the filter shape. Finally we illustrate the promising performance of MIF algorithm, equipped with high–dimensional FP filters, when applied to the decomposition of two dimensional signals.