Jaundice due to excess bilirubin buildup in neonates remains an alarming problem, especially during the very first week of postnatal life. The common method of measuring total serum bilirubin (TSB) levels involves invasive blood testing, which is time-consuming and uncomfortable for neonates. While noninvasive transcutaneous bilirubinometers (TcB) are available, that often lack accuracy due to interference from other biological chromophores. This study aims to improve bilirubin assessment by developing a noninvasive system that uses diffuse reflectance spectroscopy and a novel algorithm accounting for chromophores like melanin and hemoglobin. Focusing on the sternum as the measurement site, spectra are collected from 285 newborns. Using the proposed algorithm, the bilirubin concentration is calculated at 450, 460, and 470 nm. Compared to TSB levels, the proposed method demonstrated strong accuracy with an average bias of -0.10 mg/dL and narrower limits of agreement of 4.85 mg/dL at 470 nm.