This paper deals with the problem of precise subelliptic estimate of the \(\overline\partial\)-Neumann problem for \(n-1\) forms. We prove that in a domain \(\Omega\subseteq\mathbb{C}^ n\) which is not necessarily pseudoconvex, if near \(z_ 0\in b\Omega\) there exists a holomorphic tangential vector field \(L\) whose Levi-form is non-negative and is bounded below by a product of nonvanishing real functions, then we can find the precise subelliptic estimate \(\varepsilon\).