In a traditional fault detection and diagnosis (FDD) scheme, all of variables in a multivariate system are examined together as a single group. This FDD scheme may suffer from the amplification and masking effects that are caused by introducing fault-free variables in the fault detection index, especially for a multivariate system with a large number of variables. To overcome this problem, a new FDD scheme for multivariate systems is developed using variable grouping. First, a data-driven variable grouping algorithm is proposed to divide system variables into groups. The optimal variable grouping is obtained by maximizing variable correlations within groups but minimizing variable correlations among groups. Then, a multigroup FDD scheme is developed, consisting of an intergroup FDD method and three intragroup FDD methods, called the group-based T-2 method, the dominative latent variable method, and the intragroup regression method, respectively. Because each group consists of a few closely correlated variables, the fault detection index in every group can reduce the amplification and masking effects caused by redundant variables. This makes the fault detection index more sensitive to faults occurred in variable groups, and, hence, fault detection performance is improved. Moreover, the multigroup FDD scheme can clearly reveal the faulty groups in which faults occurred and the major contributing variables in the faulty groups. This facilitates the diagnosis of faults. The advantages of the multigroup FDD scheme are demonstrated with two case studies.