In this paper, we propose a new class of two dimensional (2D) M-channel (M-ch) non-separable filter banks (FBs) based on cosine modulated filter banks (CMFBs) via a new diagonally modulation scheme. Until now, many researchers have proposed 2D non-separable CMFBs. Nevertheless, efficient direction-selective CMFBs have not been yet. Thanks to our new modulations with diagonal shifts, proposed CMFBs have several frequency supports including direction-selective ones which cannot be realized by conventional ones. In a simulation, we show design examples of proposed CMFBs and their various directional frequency supports.