  We used the Fourier decomposition technique to investigate the stability of
the X-ray pulse profile of a young pulsar PSR B1509-58 by studying the relative
amplitudes and the phase differences of its harmonic components with respect to
the fundamental using data from the Rossi X-Ray Timing Explorer. Like most
young rotation powered pulsars, PSR B1509-58 has a high spin down rate. It also
has less timing noise allowing accurate measurement of higher order frequency
derivatives which in turn helps in study of the physics of pulsar spin down.
Detailed investigation of pulse profiles over the years will help us establish
any possible connection between the timing characteristics and the high energy
emission characteristics for this pulsar. Further, the study of pulse profiles
of short period X-ray pulsars can also be useful for using them as means of
interplanetary navigation system. The X-ray pulse profile of this source has
been analysed for 15 $ \rm years $ (1996-2011). The long term average
amplitudes of the first, second and third harmonics (and their standard
deviation for individual measurements) compared to the fundamental are 36.9 %
(1.7 %), 13.4 % (1.9 %) and 9.4 % (1.8 %) respectively. Similarly, the phases
of the three harmonics (and standard deviations) with respect to the
fundamental are 0.36 (0.06), 1.5 (0.2), 2.5 (0.3) $\rm radian $ respectively.
We do not find any significant variation of the harmonic components of the
pulse profile in comparison to the fundamental.
