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This paper introduces a new algorithm for dead reckoning navigation named Constant Velocity Update (CUPT), which is an extension of popular Zero Velocity Update (ZUPT). With a low-cost IMU (Inertial Measurement Unit) attached to a user's shoe, the proposed algorithm can efficiently reduce IMU errors by detecting not only the stance phases during walking, but also the cases at constant velocity, such as in an elevator or on an escalator. The concept, design and test of a CUPT prototype are detailed in this paper. Test results show that it can effectively detect constant velocity, and its horizontal positioning errors are below 0.45% of the total distance travelled, and vertical errors below 0.25%. This performance reached the highest accuracy in available literature.