  In a typical experiment the nuclear \mu-capture rate is determined from
measurements of the time constant of the muon decay exponential in a target. We
propose a new approach for the evaluation of the \mu-capture rate, which is
based on direct measurements of the \mu^- disappearance rate in the target.
Considering, as an example, the reaction of \mu-capture on proton, we
demonstrate that measurements of the \mu^- disappearance at different values of
the hydrogen gas pressure in the target could be used to avoid a
pressure-dependent correction and determine the "vacuum" \mu p -> \nu n
reaction rate with accuracy better than 10^{-2} after extrapolation to zero gas
density. The proposed method could be used to perform precision measurements of
the \mu^- capture rate on different types of nuclei in one experiment.
