An outer operational device includes a cover mounted to a side of a door. An actuating member is mounted in the cover and includes an end engaged with a handle to rotate therewith. A sliding member is slideably received in the cover and operably connected to the actuating member, so that the sliding member slides when the actuating member rotates. A limiting member is pivotably received in the cover between a blocking position not allowing movement of the sliding member and a release position allowing movement of the sliding member. The handle is rotatable when the limiting member is in the release position. The handle is not rotatable when the limiting member is in the blocking position. A key-operable lock core is operably connected to the actuating member, so that the limiting member can be moved to the blocking position to provide a burglarproof function.