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This paper describes the design and development of a novel robot, which attempts to emulate the basilisk lizard's ability to run on the surface of water. Previous studies of the lizards themselves have characterized their means of staying afloat. The design of a biomimetic robot utilizing similar principles is discussed, modeled, and prototyped. Functionally, the robot uses a pair of identical four bar mechanisms, with a 180 deg phase shift to achieve locomotion on the water's surface. Simulations for determining robot lift and power requirements are presented. Through simulation and experimentation, parameters are varied with the focus being a maximization of the ratio of lift to power. Four legged robots were more easily stabilized, and had a higher lift-to-power ratio than two legged robots. Decreases in characteristic length and running speed, and increases in foot diameter and foot penetration depth all cause a higher lift to power ratio. Experimental lift approached 80 gr, and experimental performance exceeded 12 gr/W for four legged robots with circular feet. This work opens the door for legged robots to become ambulatory over both land and water, and represents a first step toward robots which run on the water instead of floating or swimming.