A fault in a multivariate system is usually attributed to abnormal changes of only a small part of variables. For such a fault, the fault detection index that is defined using all variables may not have a good detection performance, due to the amplification and masking effects caused by fault-free variables. To overcome this problem, this paper proposes a multigroup fault detection and diagnosis (FDD) scheme for multivariate systems. This scheme consists of two main parts: A method for the grouping of variables, and a method to use variable groups for online FDD. In the variable grouping method, the closely correlated variables are grouped together, because the close correlations among variables are proved to be advantageous to FDD. In the online FDD method, a key group to FDD is adaptively selected for every new sample, and then FDD is performed in the key group using two types of fault detection indices that take into account the intragroup and intergroup variable correlations, respectively. Because online FDD is carried out only in one variable group, the multigroup FDD scheme has two advantages. First, the fault detection capability is improved by reducing the amplification and masking effects caused by variables in other groups. Second, fault diagnosis becomes easier because the search scope of faulty variables is narrowed down to members of the key group. These two advantages are illustrated with two case studies.