  The aim of this paper is to study the residual Monge-Amp\`{e}re mass of a
plurisubharmonic function with isolated singularity at the origin in
$\mathbb{C}^2$. We prove that the residual mass is zero if its Lelong number is
zero at the origin, provided that it is $S^1$-invariant. This result answers
the zero mass conjecture raised by Guedj and Rashkovskii in this special case.
More generally, we obtain an estimate on the residual mass by the maximal
Lelong number and Lelong number at the origin.
