  We prove that the mapping class group of a closed connected orientable
surface of genus $g$ is generated by two elements of order $g$ for $g\geq 6$.
Moreover, for $g\geq 7$ we found a generating set of two elements, of order $g$
and $g'$ which is the least divisor of $g$ such that $g'>2$. Furthermore, we
proved that it is generated by two elements of order $g/\gcd (g,k)$ for $g\geq
3k^2+4k+1$ and any positive integer $k$.
