Select the cells with the random numbers in, then:
Select the first destination cell and
Paste Special - Values
If you were doing a lot of this you could make a Macro.
Ordinary Excel formulas will retain their links to the cells containing random and will update every time anything changes and new random numbers are generated - as you probably found out.
The only answer I know, apart from the manual option given above, is to use a macro to do the equivalent of a PasteSpecial - Values.
A macro can be built-in to the worksheet, so that it runs every time cells change, but a lot depends on exactly what you are trying to do. If you want to go down this route please provide details - source cells - destination cells (and are they on the same or a different sheet). Are the cells with random numbers always the same .... and any more information to help come up with a workable solution.