An efficient quadrature formula, known as the Single-Exponential (SE) formula, was proposed by Stenger for the definite integral of an exponentially decaying function over the semi-infinite interval. The formula was derived by combining the trapezoidal formula with a SE transformation. An error bound of the formula was already given. In this study, we investigate another SE formula obtained by replacing the transformation with Muhammad-Mori's SE transformation. Its error bound was determined by theoretical analysis. Numerical comparisons of Stenger's SE formula with that of Muhammad-Mori's are given as well.