This paper proposes to use Newton-Raphson/Fisher Scoring iteration to debias/refine initial estimator of matrix completion. We prove that as long as the initial consistent estimator satisfies some loose convergence rate in Frobenius norm, we can get sharp convergence rates of the estimated factors and loadings after just one Newton-Raphson iteration. After two iterations, the estimated factors (loadings) are asymptotically equivalent to the estimated factors (loadings) if the loadings (factors) were known, and asymptotic normality of the estimated factors and loadings is obtained after up to three iterations. We also prove these results for the Fisher scoring method. Our asymptotic theory is valid under a very wide range of missing patterns, including completely random missing, selective missing, and block/staggered/periodic/switching missing. These results allow us to make statistical inference for the imputed entries and analyze the effect of using the imputed matrix on subsequent applications. We demonstrate the performance of our method by simulations and applications to the California smoking data and the stock return data.