  A new precise determination of the {\eta} meson mass is presented. It is
based on a measurement of the threshold for the {\gamma}p -> p{\eta} reaction
using the tagger focal-plane microscope detector at the MAMI-B facility in
Mainz. The tagger microscope has a higher energy resolution than the standard
tagging spectrometer and, hence, allowed an improvement in the accuracy
compared to the previous {\eta} mass measurement at MAMI-B. The result m{\eta}
= (547.851 +- 0.031 stat. +- 0.062 syst.) MeV agrees very well with the precise
values of the NA48, KLOE and CLEO collaborations and deviates by about
5{\sigma} from the smaller, but also very precise value obtained by the GEM
collaboration at COSY.
