A design method for continuous bioreactors in series with recirculation is found using Singular Value Decomposition (SVD). The optimal dilution rate and recirculation proportion which are found to maximize the productivity. Using the biomass balance equations, a set of linear equations of the form Ax = 0 is obtained. The nontrivial solution, which is obtained by a matrix null space, is dependent on the dilution rate and the recirculation proportion. Since the solution has infinite options determined by the dimension of the null space, the real biomass concentration solution is fixed by the substrate consumption and its conversion. Using an iterative method to manage the non-linear equations it is possible to obtain the non-trivial solution and to calculate the productivity, which has a maximum at an optimum dilution rate. The method obtained will help to the implementation of complex continuous bioreactors. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.