A vertical torus as above has four critical points: a, b ,c ,d. Among them, a is a local (also global) minimum, d is a local (also global) maximum, b and c are the saddle points (neither maxima nor minima) which have attracted a lot of attention since the beginning of the last century among both mathematics and physics communities. Roughly speaking, the Morse index at a critical point, say b, is the number of linearly independent directions around that critical point in which f decreases. Here, f is the function defining on the surface of the torus, whose values are exactly the altitudes of points on the surface. Accordingly to this, Morse indices of a, b, c ,d are 0, 1, 1, 2, respectively. One can easily conclude that Morse index of a local minimum is always zero.