The ages of the oldest stars shed light on the birth, chemical enrichment, and chemical evolution of the universe. Nucleocosmochronometry provides an avenue to determining the ages of these stars independent from stellar-evolution models. The uranium abundance, which can be determined for metal-poor r-process enhanced (RPE) stars, has been known to constitute one of the most robust chronometers known. So far, U abundance determination has used a single U ii line at λ3859 Å. Consequently, U abundance has been reliably determined for only five RPE stars. Here, we present the first homogeneous U abundance analysis of four RPE stars using two novel U ii lines at λ4050 Å and λ4090 Å, in addition to the canonical λ3859 Å line. We find that the U ii lines at λ4050 Å and λ4090 Å are reliable and render U abundances in agreement with the λ3859 U abundance, for all of the stars. We, thus, determine revised U abundances for RPE stars, 2MASS J09544277+5246414, RAVE J203843.2–002333, HE 1523–0901, and CS 31082–001, using multiple U ii lines. We also provide nucleocosmochronometric ages of these stars based on the newly derived U, Th, and Eu abundances. The results of this study open up a new avenue to reliably and homogeneously determine U abundance for a significantly larger number of RPE stars. This will, in turn, enable robust constraints on the nucleocosmochronometric ages of RPE stars, which can be applied to understand the chemical enrichment and evolution in the early universe, especially of r-process elements.