Hello Dowdgretch,
If I remember correctly, if you have a 24 pin power connector on the motherboard you will need a 24 pin
PSU. I am assuming when you say 20+4, the main connector is 20 pin and you have the second 4 pin connector for the part that is beside the
CPU.
It can however work the other way around. If you had a 20 pin motherboard and a 24 pin
PSU, you can still use the 24 pin
PSU connector and leave the extra pins unplugged.