Transact SQL :: Sessions Need To Have UPDLOCK To Avoid Deadlocks

The benifit of UPDLOCK is that it avoids deadlock in case both sessions run the below query at the same time.The table has clustered index on ID column

----session 1 --------
begin transaction
select * from a1

update a1
set id = 22
where id = 2

----session 2 --------
begin transaction
select * from a1

update a1
set id = 22
where id = 2

Now to avoid deadlock in the above scenario we should use (UPDLOCK) hint in the select statement.Now my question is that deadlock will be avoided in this case when both the sessions use UPDLOCK hint. If only one session uses UPDLOCk and other does not then there will be deadlock .For example session 1 uses UPDLOCK hint this will hold the U lock on the row, but the session 2 does not use this hint and apply shared lock on the same row. Now there will be deadlock when session 1 tries to update the record and is blocked by shared locks of session 2. same will be the case with session 2 and both will wait for each other and hence dead lock.so what steps can be taken to avoid deadlocks in this case. I do not want to use Snapshot isolation.