  We propose a prescription to calculate the superconformal index of the ${\cal
N}=4$ $U(N)$ supersymmetric Yang-Mills theory with finite $N$ on the AdS side.
The finite $N$ corrections are included as contributions of D3-branes wrapped
around three-cycles in $\boldsymbol{S}^5$, which are calculated as the index of
the gauge theories realized on the wrapped branes. The single-wrapping
contribution has been studied in a previous work, and we further confirm that
the inclusion of multiple-wrapping contributions correctly reproduces the
higher order terms as far as we have checked numerically.
