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We prove that the weak solution of a uniformly elliptic stochasticdifferential equation with locally smooth diffusion coefficient and H\"{o}ldercontinuous drift has a H\"{o}lder continuous density function. This resultcomplements recent results of Fournier-Printems \cite{F1}, where the density isshown to exist if both coefficients are H\"{o}lder continuous and exemplifiesthe role of the drift coefficient in the regularity of the density of adiffusion.

Local H\"{o}lder continuity property of the Densities of Solutions of SDEs with Singular Coefficients