In this paper, the main features and performances of a new numerical scheme, ILILPM (Improved Locally and Instantaneously Linearized Parabolic Model) are described. ILILPM is an improved version of the Parabolic and Backwater (PAB) and Linearized Parabolic Model (LPM) schemes, proposed in literature for the approximate solution of the Parabolic Wave model. The algorithm presented is able to take into account transcritical flow regime and transitions from free-surface to pressurized flow in tree-like channel networks. Due to its unconditional stability, the model allows large computational time steps, leading to very fast simulations during transients for a class of flow conditions larger than those solved by the parent schemes. The model is demonstrated by comparing its results with experimental observations and with the results provided by the numerical solution of the full De Saint-Venant equations.