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Jeffrey Bergstrand’s general gravity equation is used widely in studies of international trade. This note provides a correction for the special frictionless case of the gravity equation derived in Bergstrand (1985). In this particular case of perfect substitutability of goods in consumption and in production, zero tariffs, and zero transport costs, the model simplifies correctly to PXij=Yi1/2Yj1/2, not to PXij=½Yi1/2Yj1/2—the coefficient ½ should not be there. This correction has been confirmed by Professor Bergstrand. The special case has not been used much in empirical work, but a few theoretical models have used the special case and repeated the erroneous equation, so those papers too stand in need of correction. This note provides the derivations for the correction to the special frictionless case of Bergstrand’s gravity equation.