This article focuses on the problem of fusing two prior Gaussian estimates into a single estimate, when the correlation is unknown. Existing solutions either lead to a conservative fusion result, as the chosen parametrization focuses on the fusion formulas instead of correlations, or they are computationally expensive. The contribution of this article is a novel parametrization, in which the correlation is explicitly characterized a priori to deriving the fusion formulas. Then, maximizing the correlation ensures that the fusion result is based on independent parts of the prior estimates and, simultaneously, addresses the fact that the correlation is unknown. In addition, a guaranteed improvement of the accuracy after fusion is attained. An illustrative example demonstrates the benefits of the proposed method compared to an existing fusion method.