  We study non conformal negative modes of Schwarzschild black holes in the
five dimensional Einstein-Gauss-Bonnet gravity theory with a zero or negative
cosmological constant, in the context of the semiclassical quantum gravity
formulated by the path integral. We find an unique negative mode when the black
hole has a negative heat capacity which is the same in Einstein theory. On the
other hand, we still find negative modes inside a parameter region where a
small black hole has a positive heat capacity. The number is one/two for the
case of zero/negative cosmological constant respectively. In the rest of the
parameter region where the heat capacity is positive, we find no negative
modes. We discuss the possible physical understanding of having one or two
negative modes.
