Direct numerical simulations of two‐dimensional magnetohydrodynamic (MHD) flows propagating in a mean uniform magnetic field, with correlated velocity and magnetic fields are discussed. A high correlation inhibits the amount of excitation transferred to small scales, showing steeper spectral slopes at very high correlation, as in previous closure calculations. The growth of the correlation coefficient between kinetic and magnetic fields is attributed to the nondefinite positiveness of the cross correlation, which reverses its sign at small scales, because of nonlinear interactions between large and small scales in the MHD equations.