I've recently got two Rekam NEO 200 lamps with synchronization cable. To connect them to my canon 600D i've bougth an adapter.

The flash seems to sync correctly when setting exposition to values 1/320 and higher. The problem appears when i try to set exposition to 1/500 or less. With the value of 1/500 i get half of the photo black, and setting exposition to 1/1250 make the whole photo black. I'm not an expert in photography so I'm interested if it is possible to make the flash synchronize in appropriate way when exposition it set to a low value such as 1/500 or even lower?