  In this short note we are concerned with the Kahler-Einstein metrics near
cone type log canonical singularities. By two different approaches, we
construct a complete Kahler-Einstein metric with negative scalar curvature in a
neighborhood of the cone over a Calabi-Yau manifold, which provides a local
model for the future study of the global Kahler-Einstein metrics on singular
varieties. In the first approach, we show that the singularity is uniformized
by a complex ball and hence the induced metric from the Bergman metric of the
ball is a desired one. In the second approach, we obtain a complete
Kahler-Einstein metric with negative curvature by using Calabi Ansatz. At last,
we show that these two metrics are indeed the same.
