Theoretical models of very metal-poor intermediate-mass asymptotic giant branch (AGB) stars predict a large overabundance of primary nitrogen. The very metal-poor, carbon-enhanced, s-process-rich stars, which are thought to be the polluted companions of now extinct AGB stars, provide direct tests of the predictions of these models. Recent studies of the carbon and nitrogen abundances in metal-poor stars have focused on the most carbon-rich stars, leading to a potential selection bias against stars that have been polluted by AGB stars that produced large amounts of nitrogen and hence have small [C/N] ratios. We call these stars nitrogen-enhanced metal-poor (NEMP) stars and define them as having [N/Fe]>+0.5 and [C/N]<-0.5. In this paper we report on the [C/N] abundances of a sample of 21 carbon-enhanced stars, all but three of which have [C/Fe]<+2.0. If NEMP stars were made as easily as carbon-enhanced metal-poor (CEMP) stars, then we expected to find between two and seven NEMP stars. Instead, we found no NEMP stars in our sample.