In this paper, we formulate a new flux reconstruction method based on the High Dimensional Model Representation (HDMR) of the nodal flux shape. The method requires the conventional nodal parameters obtained as a result of the transverse-integration nodal solution procedure as well as corner values calculated by a combination of finite-volume and finite-difference approximations. The proposed flux reconstruction procedure is applicable to rectangular nodes and more than two energy groups. The flux reconstruction method is applied to a number of homogeneous and heterogeneous test problems in order to evaluate its accuracy.