Over 5 years of daily hard X-ray (> 20 keV) monitoring of the 2 minute
accretion-powered pulsar GX 1+4 with the Compton Gamma Ray Observator
y/BATSE large-area detectors has found nearly continuous rapid spin-do
wn, interrupted by a bright 200 day spin-up episode. During spin-down,
the torque becomes more negative as the luminosity increases (assumin
g that the 20-60 keV pulsed flux traces bolometric luminosity), the op
posite of what is predicted by standard accretion torque theory. No ch
anges in the shape of the 20-100 keV pulsed energy spectrum were detec
ted, so that a very drastic change in the spectrum below 20 keV or the
pulsed fraction would be required to make the 20-60 keV pulsed flux a
poor luminosity tracer. These are the first observations that flatly
contradict standard magnetic disk accretion theory, and they may have
important implications for understanding the spin evolution of X-ray b
inaries, cataclysmic variables, and protostars. We briefly discuss the
possibility that GX 1+4 may be accreting from a retrograde disk durin
g spin-down, as previously suggested.