The Global Positioning System (GPS) measures distances by determining the elapsed time for light to pass between the corresponding endpoints and multiplying this value with the speed of light c. An example is considered in which a metal rod and a clock are carried onboard a satellite. It is shown that Einstein’s light-speed postulate is only consistent with the deduction that the rod has increased in length at the same time that the clock has slowed down because of time dilation. Both results are independent of the orientation of the metal rod to an observer on the earth’s surface, so the above conclusion indicates that isotropic length expansion accompanies time dilation (clock riddle) on the satellite, contrary to expectations from the Fitzgerald-Lorentz length contraction (FLC) prediction of the Special Theory of Relativity (STR). This logical argument thus shows that the Lorentz transformation (LT) is self-contradictory and therefore invalid. It is also shown that the experimental results of the transverse Doppler effect are only consistent with isotropic length expansion accompanying time dilation. A GPS-compatible space-time transformation (GPSLT) is then derived that removes the contradiction of the LT while still satisfying Einstein’s two postulates of relativity.