A new modal decomposition of fluid flows, labeled cross proper orthogonal decomposition (CPOD), is presented. CPOD modes are ranked by their contributions to the trace of the cross-covariance between flow fluctuations. An application of CPOD is presented for turbulent channel flow, with modes with maximal contribution to the Reynolds shear stress. Low-order reconstructions of the velocity field using CPOD modes lead to fast convergence of the Reynolds stress and, consequently, of the turbulent mean flow.