This paper proposes a new conceptual configuration for oscillating surge wave energy converters. The concept is a self-floating device consisting of two vertical flaps with a common hinge and an averaged density equal to that of water. The two flaps will oscillate in opposite directions when driven by incident waves. Kinetic energy will be extracted from the relative speed between the two flaps by a power take-off embedded at the hinge. Numerical studies reveal that the self-floating device has a smaller resonant period and optimal power take-off damping compared with a bottom-hinged floating device of the same overall dimensions. As long as the power take-off damping is appropriately tuned, the opposite-rotation mechanism is valid in both regular and irregular waves, and no matter whether the hinge is fixed or connected with mooring lines. With the self-floating feature and opposite-rotation mechanism, the proposed concept can potentially benefit deep ocean applications by exerting a significantly less reaction loading on mooring lines and eliminating the need for a supporting frame to house the power take-off. The influence of various design parameters such as flap dimensions, submerged depth, incident wave direction, and water depth is also analyzed for a comprehensive evaluation of the proposed concept.