A way of constructing mathematically correct quantum geometrodynamics of a
closed universe is presented. The resulting theory appears to be gauge-noni
nvariant and thus consistent with the observation conditions of a closed un
iverse, by that being considerably distinguished from the traditional Wheel
er-DeWitt one. For the Bianchi-M cosmological model it is shown that a norm
alizable wave function of the universe depends on time, allows the standard
probability interpretation and satisfies a gauge-noninvariant dynamical Sc
hrodinger equation. The Wheeler-DeWitt quantum geometrodynamics is represen
ted a singular, BRST-invariant solution to the Schrodinger equation having
no property of normalizability.