In this paper, we have calculated the total gravitational radiation emitted by an axisymmetric system per unit time. Direct calculation using Hu Ning's expression for the τ(n)αβ and Bondi's cylindrical wave solution has led to -(dE)/(dt)=1/2∫x0c02sinθdθ. This result is identical with Bondi's formula that has been obtained without using any expression for the ταβ and shows that the total power radiated is always positive. The result obtained from Zheng Yu-kun's expression for the ταβ, however, does not agree with Bondi's formula and indicates that total power radiated is not always positive.