White dwarfs are the end state of the evolution of more than 97 per cent of all stars, and therefore carry information on the structure and evolution of the Galaxy through their luminosity function and initial-to-final mass relation. Examining the new spectra of all white or blue stars in the Sloan Digital Sky Survey Data Release 16, we report the spectral classification of 2410 stars, down to our identification cut-off of signal-to-noise ratio equal to three. We newly identify 1404 DAs, 189 DZs, 103 DCs, 12 DBs, and nine CVs. The remaining objects are a mix of carbon or L stars (dC/L), narrow-lined hydrogen-dominated stars (sdA), dwarf F stars, and P Cyg objects. As white dwarf stars were not targeted by SDSS DR16, the number of new discoveries is much smaller than in previous releases. We also report atmospheric parameters and masses for a subset consisting of 555 new DAs, 10 new DBs, and 85 DZs for spectra with signal-to-noise ratio larger than 10.