If South-East becomes North, North-East becomes West and so on, what will South-West become?

To find the correct direction, let's observe the angular shift described in the question:
* The original South-East (SE) direction is shifted by $135^{\circ }$ counter-clockwise to become North.
* The original North-East (NE) direction is shifted by $135^{\circ }$ counter-clockwise to become West.

Following the same pattern, we need to shift the South-West (SW) direction by $135^{\circ }$ counter-clockwise:

* Shifting SW by $45^{\circ }$ counter-clockwise gives South.
* Shifting another $90^{\circ }$ counter-clockwise gives East.

Therefore, South-West will become East.