We present a modied formulation of the dual time-stepping technique which makes use of two derivatives in pseudo-time. This new technique retains and improves the convergence properties to the stationary solution. When compared with the conventional dual time-stepping, the method with two derivatives reduces the stiness of the problem and requires fewer iterations for full convergence to steady-state. In the current formulation, these positive eects require that an approximation of the square root of the spatial operator is available and inexpensive.