An implicit time integration method for the simulation of steady and unsteady flow in pipes and channels is presented. It is based on the theory of Total Variation Diminishing (TVD) methods. A conservative linearization leads to a block tridiagonal system of equations which can be cheaply solved by means of a non-iterative matrix decomposition method. It keeps the advantages of classical implicit schemes, and properly deals with all kinds of flow. It is specially suited for steady flows including phenomena such as hydraulic jumps and also gives satisfactory results for time dependent problems. Several test cases are shown to illustrate the performance of this implicit technique in single channels and networks.