  In this article, we aim to study decoupling inequality for a specific
degenerate hypersurface in $\mathbb{R}^4$. Inspired by the work of
Bourgain--Demeter and Li--Zheng, we consider the hypersurface
$\mathcal{S}^3_{4}:=\{(\xi_1,\xi_2,\xi_3,\xi^4_1+\xi^4_2+\xi^4_3):0\leq
\xi_j\leq1, \text{for}~j=1,2,3\}$ in $\mathbb{R}^4$ and study decoupling
estimates.
