Summary: The difficulty that there don’t exist global solutions to \(\overline\partial\)-equation on a general bounded domain is overcome. The following result is obtained. Let \(D\) be a bounded domain in \(C^n\), \(\partial D\in C^{(1)}\), \(g\in C^{(\infty)}_{0,1}(\overline D)\) such that \(\overline\partial g= 0\), then there exists a local differential solution of equation \(\overline\partial u= g\), in \(D\) which is \[ u= -\int_D g(\xi)\wedge \Omega(h)- \int_{\partial D}g(\xi)\wedge \int^1_0 \Omega(H) \] and \(u\) has an inner closed uniform estimate in \(D\), i.e. \(\|u\|\leq C\|g\|\) where \(\Omega(h)\) and \(\Omega(H)\) are Bochner-Martinelli kernel and discrete kernel, respectively.