Press down on the tab and have the end of the clip move out as to no longer be in contact with the socket then release the clip. Kinda surprised that someone would ask this, when all else fails you can always press either side of the clip and release from the socket.

If I remember correctly, and in all probability I do, the intended way is to remove the fan and then pull up the green thingie.
Those were one of the nicest intel coolers ever in terms of installation, so easy and without bending and pushing metal hooks.

Not a fan of this design. Coppermine core is very fragile and it's very easy to damage it, when demounting such cooler.

nforce4max:
clip doesn't move one bit when I press really hard. That's why I'm asking. Don't want break anything.

konc:
yes, it looks like this. I guess the fan must be removed first.

The Serpent Rider:
Tualeron is installed

Main thing is to get the clip loose, once that has happened you can twist the cooler off the CPU, it has most probably firmly "glued" itself to the CPu much like you see on lot of AMD CPUs later on. I definitely remember having to do it with all Tualatins and Tualerons when getting their heatsink off for the first time.

You could unclip the fan off the top of the heatsink first, might save it from damage if force needs to be applied. Just squeeze it in on one side first.

Nothing like seeing the CPU pop out of the socket when you loosen the heatsink and pull it out.

My mind has been tired lately but yes should have removed the fan and pull up on the green lever, my advice earlier is for the vastly more common clip design but hopefully it might help newer people someday.