A plausible "s"-factor solution for many types of psychological and educational tests is one in which there is one general factor and "s - 1" group- or method-related factors. The bi-factor solution results from the constraint that each item has a non-zero loading on the primary dimension "alpha(sub j1)" and at most one of the "s - 1" group factors. This structure has been termed the "bi-factor" solution by K. J. Holzinger and F. Swineford (1937), but it also appears in the work of L. R. Tucker and K. G. Joreskog. All attempts at estimating the parameters of this model have been restricted to continuously measured variables; it has not been previously considered in the context of item response theory (IRT). It is conceivable that the bi-factor structure might arise in IRT-related problems. The purpose of this paper is to derive a bi-factor item response model for binary response data, and to develop a corresponding method of parameter estimation. This restriction leads to a major simplification of the likelihood equations that: (1) permits the statistical evaluation of problems of unlimited dimensionality; (2) permits conditional dependence among discrete and previously identified subsets of items; and (3) in some cases, provides more parsimonious factor solutions than an unrestricted full-information item factor analysis might provide. (Author/RLC)