In this paper, we present a single actuator wave-like robot, a novel bioinspired robot which can move forward or backward by producing a continuously advancing wave. The robot has a unique minimalistic mechanical design and produces an advancing sine wave, with a large amplitude, using only a single motor but with no internal straight spine. Over horizontal surfaces, the robot does not slide relative to the surface and its direction of locomotion is determined by the direction of rotation of the motor. We developed a kinematic model of the robot that accounts for the two-dimensional mechanics of motion and yields the speed of the links relative to the motor. Based on the optimization of the kinematic model, and accounting for the mechanical constraints, we have designed and built multiple versions of the robot with different sizes and experimentally tested them (see movie). The experimental results were within a few percentages of the expectations. The larger version attained a top speed of 57 cm s−1 over a horizontal surface and is capable of climbing vertically when placed between two walls. By optimizing the parameters, we succeeded in making the robot travel by 13% faster than its own wave speed.