By doing what? Yes and no is the answer.
Whether it actually fits your existing motherboard or works is dependant on the board the CPU fits into and possibly its BIOS revision - many P4s were socket 478 CPUs and you'd have fun trying to fit an E4600 into one of those
To work things out, you'd need to use the Intel website for your board (it is an Intel branded board in the first place isn't it?) and click the appropriate link for processor compatibility or you can go here: http://processormatch.intel.com/CompDB/SearchResult.aspx?ProcNbr=E4600&wapkw=(E4600) . Of course if your existing board turns out not to be compatible but you buy one that is for the new CPU then you can also go ahead. Thats about as helpful as I can be with the very limited info you've given in your question.