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Pulse profiles of X-ray pulsars play an important role in X-ray pulsar based navigation (XPNAV) and studying the rotation and emission characteristics of the pulsars.In this paper,we present an X-ray timing analysis of the young Crab-like pulsar PSR B1509-58 by using archival Rossi X-ray Timing Explorer (RXTE) data.We have investigated the stability of the PSR B1509-58 pulse profile in the energy band of 2- 60keV.The analysis results show that in the energy band of 2-30keV,the flux of pulse is the largest than the others,and the 2-30keV energy band possess the most photon series in 2-60keV.Furthermore,as the energy range increases,the Pearson's correlation,between the standard pulse profile and the integrated pulse profiles of different energy band,varies small,all the Pearson's correlations in different energy range are above 0.99,meanwhile,in the energy ranges of 2-30keV,there is no phase delay between the integrated pulse profile and the standard pulse profile,which means that the pulse profile is stable.Furthermore,pulse width of the pulsar profiles in different energy ranges is studied.The analysis results show that the pulse widths are narrowed as the energy ranges increase.