The Blinder-Oaxaca decomposition technique is widely used to identify and quantify the separate contributions of differences in measurable characteristics to group differences in an outcome of interest. The use of a linear probability model and the standard Blinder-Oaxaca decomposition, however, can provide misleading estimates when the dependent variable is binary, especially when group differences are very large for an influential explanatory variable. A simulation method of performing a nonlinear decomposition that uses estimates from a logit, probit or other nonlinear model was first developed in a Journal of Labor Economics article (Fairlie 1999). This nonlinear decomposition technique has been used in nearly a thousand subsequent studies published in a wide range of fields and disciplines. In this paper, I address concerns over path dependence in using the nonlinear decomposition technique. I also present a straightforward method of incorporating sample weights in the technique.