When a person was arranged for the burial process, the person was alid upon a very long cloth which was twice the height of the person, then the cloth was folded over the front of the person. When Jesus's boidy was removed from the cross, it is likely that He was laid upon such a span of cloth, BEFORE having his body cleansed, wrapped, and anointed with scents to cover the smell of death. The scenting oils were used because somoen would return periodically to the dessicated body for anointing and 'tending', until just the bones were left and these were then often placed in an ossuary(sp?).
BTW, in the Greek, the scene confers a sense of the wrappings were still int he shape of a man, so it is believed Jesus elft the wrappings without unwrapping them, and the head wrapping was found separate fromt he body wrappings. The cloth onto which He would have been placed to transport Him fromt Golgotha would be the Shroud of Turin.