The results of a neutrino experiment that involved 24.12 yr of live time of observation of muons from the lower Earth’s hemisphere with the aid of the Baksan Underground Scintillator Telescope are presented. In the problem of searches for a signal from the annihilation of dark matter in the Sun, an upper limit on the cross section for the elastic scattering of a weakly interacting massive particle (WIMP) on a nucleon was obtained at a 90% confidence level from an analysis of data accumulated within 21.15 yr of live time of observation. A neutralino in a nonminimal supersymmetric theory was considered for a WIMP. The best limit at the Baksan Underground Scintillator Telescope on the cross section for spin-dependent neutralino interactionwith a proton corresponds to 3×10−4 pb for the neutralino mass of 210 GeV/c2. This limit is three orders of magnitude more stringent than similar limits obtained in experiments that detected directly WIMP scattering on target nuclei.