Recently, there has been a growing interest in the use of orthogonal rational functions (ORFs) in system identification. There are many advantages over more classical techniques. Probably due to a known explicit expression for the basis functions when the orthogonality weight is uniformly equal to 1 (the so called Malmquist basis), the attention has been on the development of methods using this basis. However, for some discrete identification problems, this choice of the orthogonality weight may still lead to serious numerical problems due to the ill conditioning of the linear system of equations to be solved. In this note, we give an algorithm based on a more general system of ORF to overcome the numerical problem and which allows for a fast-order update of the estimate.