  RX J0806+15 has recently been identified as the binary system with the
shortest known orbital period. We present a series of observations of RX
J0806+15 including new optical observations taken one month apart. Using these
observations and archival data we find that the period of this system is
decreasing over time. Our measurements imply f_dot = 6.11x10^-16 Hz/s, which is
in agreement with a rate expected from the gravitational radiation for two
white dwarfs orbiting at a given period. However, a smaller value of f_dot =
3.14x10^-16 Hz/s cannot be ruled out. Our result supports the idea that the
321.5 s period is the orbital period and that the system is the shortest period
binary known so far and that it is one of the strongest sources of constant
gravitational radiation in the sky. Furthermore, the decrease of the period
strongly favours the unipolar inductor (or electric star) model rather than the
accretion models.
