The recent boom in micro-computer hardware giving computing power unexpected some fifteen years ago, permits nowadays all engineering firms, if not individuals, to solve large scale problems. As a result, methods disregarded in the early seventy's now become attractive. One of those is the element method for pipe network analysis which is appealing when one considers not only network flow balancing but shock waves propagation analysis and storing of the network in a data base for quick references or modification of the system layout. The proposed modified method addresses the convergence behaviour by using a Newton- Raphson procedure on the residue of a partionned matrix system. Reordering of the elements gives a submatrix topology of particular types that can be inverted with efficient algorithms. It results in a matrix, the order of which corresponds to the number of loops in the system, to be inverted during the iterative process. Two examples, taken from previous papers, are analysed and discussed.