  We report on XMM-Newton observations of the Black Widow pulsar, PSR B1957+20.
The pulsar's X-ray emission is non-thermal and best modeled with a single
powerlaw spectrum of photon index 2.03^{+0.51}_{-0.36}. No coherent X-ray
pulsations at the pulsar's spin-period could be detected, though a strong
binary-phase dependence of the X-ray flux is observed for the first time. The
data suggest that the majority of the pulsar's X-radiation is emitted from a
small part of the binary orbit only. We identified this part as being near to
where the radio eclipse takes place. This could mean that the X-rays from PSR
B1957+20 are mostly due to intra-shock emission which is strongest when the
pulsar wind interacts with the ablated material from the companion star.
