To understand the first stars and galaxies of the early universe, we would like to measure the highly redshifted line of neutral hydrogen. The Hydrogen Epoch of Reionization Array (HERA) is a dedicated instrument that measures the power spectrum of the highly redshifted 21-cm emission line of hydrogen. It is a low-frequency radio interferometer, currently under construction in South Africa on the site of the future SKA. When complete, HERA will comprise 350 14-meter antennas operating from 50 - 225 MHz. The data here is taken from the well-characterized commissioning data of a 19-element hexagonal close-packed subarray operating from 110 - 190 MHz (as described in Kohn et al. 2019; ApJ 882:58) over seven nights. The problem we address is the necessity of calibrating polarization accurately in order to understand how polarized sources will corrupt our measurements. This requires a fully polarized calibration scheme, which is different than the standard HERA pipeline (Dillon et al. 2020, MNRAS accepted; Kern et al. 2020, ApJ 890:122). We have implemented a version of the calibration based on Smirnov & Tasse 2015; MNRAS 449:2668. We expect that this will improve the calibration of Stokes U and V, which showed evidence of poorly determined relative phases between linear polarizations (Tucker et al. 2019; AAS #235, 177.05). We have tested this calibration technique on a simulated visibilities and gains (Jones matrices) of the HERA-19 array and found convergence, but the process still needs to be streamlined. We are currently exploring applying the technique to real data and comparing it against the previous calibration scheme.