  Based on a deep ROSAT HRI observation, we have detected a pulsed signal in
the 0.1-2 keV band from PSR J0537-6910 --- the recently discovered pulsar
associated with the supernova remnant N157B in the Large Magellanic Cloud. The
measured pulse period 0.01611548182 ms (+- 0.02 ns), Epoch MJD 50540.5, gives a
revised linear spin-down rate of $5.1271 \times 10^{-14} s s^{-1}$, slightly
greater than the previously derived value. The narrow pulse shape (FWHM = 10%
duty cycle) in the ROSAT band resembles those seen in both XTE and ASCA data (>
2 keV), but there is also marginal evidence for an interpulse. This ROSAT
detection enables us to locate the pulsar at R.A., Dec (J2000) =
$5^h37^m47^s.2, -69^\circ 10' 23''$. With its uncertainty $\sim 3''$, this
position coincides with the centroid of a compact X-ray source. But the pulsed
emission accounts for only about 10% of the source luminosity $\sim 2 \times
10^{36} ergs^{-1}$ in the 0.1-2 keV band. These results support our previous
suggestions: (1) The pulsar is moving at a high velocity ($\sim 10^3 km/s$);
(2) A bow shock, formed around the pulsar, is responsible for most of the X-ray
emission from the source; (3) A collimated outflow from the bow shock region
powers a pulsar wind nebula that accounts for an elongated non-thermal radio
and X-ray feature to the northwest of the pulsar.
