QTL mapping with statistical likelihood-based procedures or asymptotically equivalent regression methods is usually carried out in a univariate way, even if many traits were observed in the experiment. Some proposals for multivariate QTL mapping by an extension of the maximum likelihood method for mixture models or by an application of the canonical transformation have been given in the literature. This paper describes a method of analysis of multitrait data sets, aimed at localization of QTLs contributing to many traits simultaneously, which is based on the linear model of multivariate multiple regression. A special form of the canonical analysis is employed to decompose the test statistic for the general no-QTL hypothesis into components pertaining to individual traits and individual, putative QTLs. Extended linear hypotheses are used to formulate conjectures concerning pleiotropy. A practical mapping algorithm is described. The theory is illustrated with the analysis of data from a study of maize drought resistance.