Without measurement errors in predictors, discontinuity of a non- parametric regression function at unknown locations could be esti- mated using a number of existing approaches. However, it becomes a challenging problem when the predictors contain measurement errors. In this paper, an error-in-variables jump point estimator is suggested for a nonparametric generalized error-in-variables regression model. A major feature of our method is that it does not impose any parametric distribution on the measurement error. Its performance is evaluated by both numerical studies and theoretical justifications. The method is applied to studying the impact of Medicare Levy Surcharge on the private health insurance take-up rate in Australia.