We present a catalog of hard X-ray sources in a square-degree region surveyed by NuSTAR in the direction of the Norma spiral arm. This survey has a total exposure time of 1.7 Ms, and typical and maximum exposure depths of 50 ks and 1 Ms, respectively. In the area of deepest coverage, sensitivity limits of $5times10^{-14}$ and $4times10^{-14}$ erg s$^{-1}$ cm$^{-2}$ in the 3-10 and 10-20 keV bands, respectively, are reached. Twenty-eight sources are firmly detected and ten are detected with low significance; eight of the 38 sources are expected to be active galactic nuclei. The three brightest sources were previously identified as a low-mass X-ray binary, high-mass X-ray binary, and pulsar wind nebula. Based on their X-ray properties and multi-wavelength counterparts, we identify the likely nature of the other sources as two colliding wind binaries, three pulsar wind nebulae, a black hole binary, and a plurality of cataclysmic variables (CVs). The CV candidates in the Norma region have plasma temperatures of $approx$10-20 keV, consistent with the Galactic Ridge X-ray emission spectrum but lower than temperatures of CVs near the Galactic Center. This temperature difference may indicate that the Norma region has a lower fraction of intermediate polars relative to other types of CVs compared to the Galactic Center. The NuSTAR log$N$-log$S$ distribution in the 10-20 keV band is consistent with the distribution measured by Chandra at 2-10 keV if the average source spectrum is assumed to be a thermal model with $kTapprox15$~keV, as observed for the CV candidates.
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