We have addressed the issue of field redefinition in connection with renormalisability. Our study is restricted to theories of interacting scalar fields. We have, in particular, shown that if a theory is renormalisable in the usual power-counting sense then it remains renormalisable in the same sense after a change of variables. This is due to the use of the powerful method of the background field expansion. In the case of a single complex sclar field, it turns out that the determination of the counter-terms is much simpler when polar coordinates are used. We illustate this by carrying out a one-loop calculation in the latter case.