The High-Speed Photometer (HSP) on board the Hubble Space Telescope (HST) observed the 50 ms pulsar B0540-69 in the Large Magellanic Cloud on 1993 August 26 for 1 hr in a passband extending from 1600 Å to 7000 Å. The pulse profile resembles both that in the optical region alone and in the X-ray region. The pulsed fraction in the UV-plus-visible passband is 0.16±0.02, similar to that measured in the X-ray region. The pulsar frequency on MJD 49225.2557 (start time of the observation) was 19.83448±0.00002 Hz. When we combine our observed frequency with other published X-ray and optical observations and assume no discontinuities (glitches) in the spin-down rate since 1979, we derive a braking index n = 2.28±0.02.