A spectroscopic study was carried out for the double-line A-type eclipsing binary system RR Lyn A \(+\) B based on the disentangled spectra, with an aim of clarifying the differences in photospheric chemical compositions between the components, where \(T_\textrm{eff}\) (effective temperature) and \(v_\textrm{t}\) (microturbulence) were determined from Fe lines. The resulting abundances of 30 elements revealed the following characteristics. (1) The brighter/hotter A shows metal-rich trends of classical Am stars; i.e., heavier elements generally show overabundances tending to increase towards higher Z (atomic number) with exceptionally large deficit of Sc, while light elements such as CNO show underabundances. (2) Meanwhile, the abundances of fainter/cooler B are closer to the solar composition ([X/H] \(\sim 0\) for intermediate Z elements such as Fe group) though [X/H] does exhibit a slightly increasing tendency with Z, which suggests that B is a kind of marginal Am star with almost normal metallicity. This consequence is in contrast to the results of previous studies, which reported B to be of a metal-deficient nature similar to \(\lambda \) Boo stars. Such distinctions of chemical abundances between A and B may serve as a key to understanding the conditions for the emergence of the Am phenomenon.