We present the results of a new analysis of data taken in 1998-2002 for a search for high-energy extraterrestrial neutrinos. The analysis is based on a full reconstruction of high-energy cascade parameters: vertex coordinates, energy and arrival direction. Upper limits on the diffuse fluxes of all neutrino flavors, predicted by several models of AGN-like neutrino sources are derived. For an ${bf E^{-2}}$ behavior of the neutrino spectrum, our limit is ${bf E^{2} F_{ u}(E) < 2.9 times 10^{-7}}$ cm${bf ^{-2}}$ s${bf ^{-1}}$ sr${bf ^{-1}}$ GeV over a neutrino energy range ${bf 2 times 10^4 div 2 times 10^7}$ GeV. This limit is by a factor of 2.8 more stringent than a limit obtained with a previous analysis.
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