The quasidiffusion (QD) method is an established and efficient iterative technique for solving particle transport problems. Each QD iteration consists of a high-order SN sweep, followed by a low-order QD calculation. QD has two defining characteristics: (1) its iterations converge rapidly for any spatial grid and (2) the converged scalar fluxes from the high-order SN sweep and the low-order QD calculation differ, by spatial truncation errors, from each other and from the scalar flux solution of the SN equations. In this paper, we show that by including a transport consistency factor in the low-order equation, the converged high-order and low-order scalar fluxes become equal to each other and to the converged SN scalar flux. However, the inclusion of the transport consistency factor has a negative impact on the convergence rate. We present numerical results that demonstrate the effect of the transport consistency factor on stability.