A process for the preparation of 1,2-benzisoxazole-3-methanesulfonamide without isolation of intermediates in solid form, by using 4-hydroxycoumarin as a starting compound, and water and 1,2-dichloroethane as solvents; and an industrially useful process for the preparation of 1,2-benzisoxazole-3-acetic acid, by reacting 4-hydroxycoumarin and hydroxylamine in water.