The expected profit or loss of a non-life insurance company is determined for the whole of its multiple business lines. This implies the study of the claims reserving problem for a portfolio consisting of several correlated run-off triangles. A popular technique to deal with such a portfolio is the multivariate chain-ladder method of Merz and Wuthrich (2008). However, it is well known that the chain-ladder method is very sensitive to outlying data. For the univariate case, we have already developed a robust version of the chain-ladder method. In this article we propose two techniques to detect and correct outlying values in a bivariate situation. The methodologies are illustrated and compared on real examples from practice. (C) 2011 Elsevier B.V. All rights reserved.