If those are surfaces, the arrows you indicate aren’t really normals… According to your image, there could be one of 4 possible logical directions for those ‘squares’ and none of them are normal to the surfaces - the normal being perpendicular to those (i.e. in and out of the page).
Ah yes… thank for clarifying. . .i should of used a better image. This is a top down view and the surfaces are actually boxes. . sorry for the confusion!
… six possible directions then 
direction is specified in the image
In my opinion : The reference should be a line, the object (selected) line, (choice: + or -)
Maybe I’m wrong because of the 3D space consideration ?
Ideally the box would be in a block.
To move in the local direction, enter the block by double clicking. Move, exit the block and voilà.
Thank you sir. Impressive! That pretty much what i was getting at. @martinsiegrist