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A way of constructing mathematically correct quantum geometrodynamics of aclosed universe is presented. The resulting theory appears to begauge-noninvariant and thus consistent with the observation conditions of aclosed universe, by that being considerably distinguished from the conventionalWheeler - DeWitt one. For the Bianchi-IX cosmological model it is shown that anormalizable wave function of the Universe depends on time, allows the standardprobability interpretation and satisfies a gauge-noninvariant dynamicalSchrodinger equation. The Wheeler - DeWitt quantum geometrodynamics isrepresented by a singular, BRST-invariant solution to the Schrodinger equationhaving no property of normalizability.Comment: LaTeX, 18 pages, to be published in Int. J. Mod. Phys.

QUANTUM GEOMETRODYNAMICS OF THE BIANCHI-IX MODEL IN EXTENDED PHASE SPACE