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.
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