The result of a measurement of the period of rotation of Jupiter's inner magnetosphere with unprecendented precision is presented. The measurement was made from the University of Florida database of 35 apparitions of Jovian decametric observations at frequencies of 18, 20, and 22 MHz between 1957 and 1994. The mean of our 24 independent measurements was 9h55m29s.685, and the standard deviation of the mean was 0s.0034. The System III (1965) Jovian rotation period value that is currently accepted by the International Astronomical Union is greater than our value by 7.4 times our standard deviation; it appears to be in need of revision. We set an upper limit of 27 milliseconds per year on a possible drift of the rotation period as measured by our method. ¿ American Geophysical Union 1996