We have studied the dependence of the high frequency Quasi-periodic Oscillation (QPO) (~284 Hz) on the phase of the low frequency QPO (~6 Hz) in the black hole X-ray binary XTE J1550-564 in the observations of the Rossi X-ray Timing Explorer (RXTE) performed on MJD 51241. By selecting the local maxima and the local minima in the light curve on the 6 Hz QPO time scale, we have found the corresponding high frequency QPO frequencies are consistent within 1.5 sigma. However, the average central QPO ...