T-SQL (SS2K8) :: Renumbering Remaining Records In A Table After Some Records Deleted

I have a table with about half a million records, each representing a patient in my county.

Each record has a field (RRank) which basically sorts the patients as to how "unwell" they are according to a previously-applied algorithm. The most unwell patient has an RRank of 1, the next-most unwell has RRank=2 etc.

I have just deleted several hundred records (which relate to patients now deceased) from the table, thereby leaving gaps in the RRank sequence. I want to renumber the remaining recs to get rid of the gaps.

I can see what I want to accomplish by using ROW_NUMBER, thus:

SELECT ROW_NUMBER() Over (ORDER BY RRank) as RecNumber, RRank
FROM RPL
ORDER BY RRank

I see the numbers in the RecNumber column falling behind the RRank as I scan down the results

My question is: How to convert this into an UPDATE statement? I had hoped that I could do something like:

UPDATE RISC_PatientList_TEMP
SET RRank = ROW_NUMBER() Over (ORDER BY RRank);

but the system informs that window functions will only work on SELECT (which UPDATE isn't) or ORDER BY (which I can't legally add).