The solar spectrum is a key parameter for different scientific disciplines such as solar physics, climate research, and atmospheric physics. The SOLar SPECtrometer (SOLSPEC) instrument of the Solar Monitoring Observatory (SOLAR) payload onboard the International Space Station (ISS) has been built to measure the solar spectral irradiance (SSI) from 165 to 3088 nm with high accuracy. To cover the full wavelength range, three double-monochromators with concave gratings are used. We present here a thorough analysis of the data from the third channel/double-monochromator, which covers the spectral range between 656 and 3088 nm. A new reference solar spectrum is therefore obtained in this mainly infrared wavelength range (656 to 3088 nm); it uses an absolute preflight calibration performed with the blackbody of the Physikalisch-Technische Bundesanstalt (PTB). An improved correction of temperature effects is also applied to the measurements using in-flight housekeeping temperature data of the instrument. The new solar spectrum (SOLAR–IR) is in good agreement with the ATmospheric Laboratory for Applications and Science (ATLAS 3) reference solar spectrum from 656 nm to about 1600 nm. However, above 1600 nm, it agrees better with solar reconstruction models than with spacecraft measurements. The new SOLAR/SOLSPEC measurement of solar spectral irradiance at about 1600 nm, corresponding to the minimum opacity of the solar photosphere, is 248.08 ± 4.98 mW m−2 nm−1 (1 σ), which is higher than recent ground-based evaluations.