We study a finite, divergence-free approach to renormalisation originally proposed in the early '70s by Blaer and Young, and Callan. It is based on equations similar to the Callan-Symanzik equations and introduced in the context of the & lambda;& phi;4 theory. We generalise this method to the case of two interacting scalar fields, with obvious generalisation to an arbitrary number of fields.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.