Sodium-rich stars are often found in globular clusters giants. However, some sodium-rich stars have been found among field metal-poor stars. These stars are considered as evaporated from globular clusters. Identified such kind of stars among the field stars in the Galaxy may provide insights of which mechanism was responsible for the ejection from a globular cluster and may reveal some chemical peculiarity. Therefore, we started a search, using high-resolution spectroscopy, among metal-poor stars from several sources of the literature to find a sodium-rich star. Here we present the results for the temperature, gravity, metallicity, and sodium abundances for the stars of our sample. For many of them we determined the temperature, gravity, metallicity, and sodium abundances for the first time. As a result of our search we found one star, CD-23°16310, which has a [Na/Fe] ratio of +1.09. We also show that CD-23°16310 is not a carbon-enhanced metal-poor (CEMP) star since carbon is not enriched but is nitrogen-rich. We did not detect any variation of the radial velocity that would support the hypothesis of mass transfer. Thus, the high sodium and nitrogen abundance could be due to a strong internal mixing process, suggesting that CD-23°16310 is an early asymptotic giant branch star.