Heritable quantitative characters underline complex genetic traits. However, a single quantitative phenotype may not be a suitably good surrogate for a clinical end point trait. It may be more optimal to use a multivariate phenotype vector correlated with the end point trait to carry out an association analysis. Existing methods, such as variance components and principal components, suffer from inherent limitations, such as lack of robustness or difficulty in biological interpretation of association findings. In an effort to circumvent these limitations, we propose a novel regression approach based on a conditional binomial model to detect association between a single-nucleotide polymorphism and a multivariate phenotype vector. We use our proposed method to analyze data on systolic and diastolic blood pressure levels provided in Genetic Analysis Workshop 18. We find that the bivariate analysis of the two phenotypes yields more promising results in terms of lower p-values compared to univariate analyses.