1. Right click Start Menu
2. Tick both boxes under Privacy
3. Click Apply
4. Click Customize
5. On the bottom you will see "Number of recent programs to display" and "Number of recent items to display in Jump Lists" - set both of them to a number smaller than the amount of pinned programs. 0 worked for me.
6. Click OK
7. Click Apply
8. Un-tick both boxes under Privacy
9. Click Apply
10. Click OK
If you set them to 0, the space will be gone without un-ticking the boxes. But since you don't want any recent things displayed, there is no point in leaving them ticked.
I had the same problem as ttarvi. If I had less than 9 programs pinned, there was a blank space. If I remember correctly the default number for "recent items" was 10. I did as ttarvi suggested and the blank space was gone.
If you want the space back, you tick one of the boxes, set a high number (try 50
), and un-tick the box.