A rapid, stable decoupled algorithm for solving semiconductor hydrodynamic equations is proposed. First, the Newton iterations to solve each set of equations are omitted. This causes no change in obtained solutions nor in the block convergence. Second, in place of the exact Jacobian matrix, a reduced Jacobian matrix is constructed and used to solve the energy balance equation. This reduced-Jacobian-matrix method is applied to two different hydrodynamic formulations and shown to be very effective, in both formulations, in accelerating the block convergence speed of the decoupled algorithm. The method provides an efficient version of the decoupled algorithm, which is very simple and applicable to a large variety of hydrodynamic formulations.>