The Photoshop Offset dialogue

Corel Photo-Paint: Effects/2D Effects/Offset

Adobe Photoshop: Filter/Other/Offset
 

The essential tool for producing seamless tiles. At the  50/50 setting it will put the top left hand quarter of the image down to the bottom right, top right to bottom left, etc. Horizontal numbers offset side to side, vertical top to bottom. The numbers relate to the percentage of offset, 50 being half way. Make sure the 'Wrap Around' button is checked.

The Corel Photo-Paint Offset dialogue

Offset Horizontal 0, Vertical 50

   Offset Horizontal 50, Vertical 0