MAX() and GROUP BY question

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Hello everybody
Can you explain me please how to get the entire row where ID is maximum per given
status_id
Mysql 4.0.xx 

for example:

id status_id    name        date
6     3           name0      date0
5     1           name1      date1
7     4           name3      date3
10   3           name2      date2

If I execute 

SELECT MAX(id), status, name, date FROM table_name WHERE status=3 GROUP BY staus_id
or
SELECT MAX(id), status, name, date GROUP BY staus_id

only id and status_id will be returned correctly, while name and date can well be from
another row
for example: 10 3 name0 date0


Thanks a lot for any suggestions
Yannis