From the GOES-12/SXI data, we studied the initial stage of motion for six rapid (over 1500 km/s) halo coronal mass ejections (HCMEs) and traced the motion of these HCMEs within the SOHO/LASCO C2 and C3 field-of-view. For these HCMEs the time-dependent location, velocity and acceleration of their fronts were revealed. The conclusion was drawn that two types of CME exist depending on their velocity time profile. This profile depends on the properties of the active region where the ejection emerged. CMEs with equal ejection velocity time dependence originate form in the same active region. All the HCMEs studied represent loop-like structures either from the first moment of recording or a few minutes later. All the HCMEs under consideration start their translational motion prior to the associated X-ray flare onset. The main acceleration time (time to reach the highest velocity within the LASCO/C2 field-of-view) is close to the associated flare X-ray radiation intensity rise time. The results of (Zhang and Dere, 2006) on the existence of an inverse correlation between the acceleration amplitude and duration, and also on the equality of the measured HCME main acceleration duration and the associated flare soft X-ray intensity rise time are validated. We established some regularities in the temporal variation of the angular size, trajectory, front width and the HCME longitude-to-cross size ratio.