This article describes a robot walker based on a new single degree-of-freedom six-bar leg mechanism that provides rectilinear, non-rotating, movement of the foot. The walker is statically stable and requires only two actuators, one for each side, to provide effective walking movement on a flat surface. We use Curvature Theory to design a four-bar linkage with a flat-sided coupler curve and then adds a translating link so that walker foot follows this coupler curve in rectilinear movement. A prototype walker was constructed that weighs 1.6 kg, is 180 mm tall, and travels at 162 mm/s. This is an innovative legged robot that has a simple reliable design.