This paper introduces scalar projection scale (SPS for short) parameter for rational Bézier curves. An open rational Bézier curve is SPS parameterized iff its weights fulfill some constraints. SPS parameter is geometric, and with which the rational Bézier curve possesses single-value, location, symmetry, and control point adjustment properties. Using SPS parameter, it is easy to construct single-value curve, perform point-curve test, and adjust shape of curve. A necessary and sufficient condition for SPS reparameterization is also given. Linear and quadratic rational Bézier curves parameterized and reparameterized by SPS are discussed.