A high-resolution stigmatic spectrometer, the High Resolution Telescope and Spectrograph (HRTS), has been calibrated against broad-band irradiance measurements of the Sun with the Solar Ultraviolet Irradiance Monitor (SUSIM) and the Solar-Stellar Irradiance Comparison Experiment (SOLSTICE), resulting in a new value for the radiance of the solar UV continuum from 1500 to 1700 angstrom. Previous HRTS results were based on a comparison with the Skylab SO82B calibration rocket, CALROC, and agreed, within the stated accuracy of +/- 25%, with other independently calibrated UV radiance measurements over the last 20 years. The new calibration increases the derived radiance in this wavelength range by a factor of 1.35-1.5 over previous measurements. The difference is systematic over the wavelength range and cannot be explained by contributions to the irradiance from spectral lines or enhanced emission in active regions. The new radiance values are significant for solar atmospheric models as well as for related studies of stellar models, since the radiance at these wavelengths reflects the value of the minimum temperature at the top of the photosphere.