Because it is difficult to ascertain the dimensionality of a test composed of binary items through the use of factor analysis alone, a method is proposed that combines item characteristic curve (ICC) theory with factor analysis. Factor structure of tetrachoric correlations is distorted by non-normal distribution of ability. Item characteristics curve theory cannot demonstrate multidimensionality. Therefore, a model is proposed in which the item score is expressed as the sum of an ICC function representing the general factor, and a residual obeying a linear factor model. The former is calculated using estimated ability and subtracted from the observed item score to obtain the residual. Residuals are factor analyzed by standard methods. An illustration is provided using reading and mathematics items. The results show that the variance due to factors specific to subtests is small compared to error even when subtests differ widely in content. (Author/CTM)