  A way of constructing mathematically correct quantum geometrodynamics of a
closed universe is presented. The resulting theory appears to be
gauge-noninvariant and thus consistent with the observation conditions of a
closed universe, by that being considerably distinguished from the conventional
Wheeler - DeWitt one. For the Bianchi-IX cosmological model it is shown that a
normalizable wave function of the Universe depends on time, allows the standard
probability interpretation and satisfies a gauge-noninvariant dynamical
Schrodinger equation. The Wheeler - DeWitt quantum geometrodynamics is
represented by a singular, BRST-invariant solution to the Schrodinger equation
having no property of normalizability.
