UPDATE FROM problem, multiple updates of same row don't seem to work

Here is an example:

CREATE TABLE tablea(id int PRIMARY KEY,flag int
);

CREATE TABLE tableb(aid int REFERENCES tablea(id),flag int
);

INSERT INTO tablea VALUES(1,0);
INSERT INTO tablea VALUES(2,0);

-- Flags for 1st row of tablea - When ORed, should be 7
INSERT INTO tableb VALUES(1,1);
INSERT INTO tableb VALUES(1,2);
INSERT INTO tableb VALUES(1,4);

-- Flags for 2nd row of tablea - When ORed, should be 5
INSERT INTO tableb VALUES(2,1);
INSERT INTO tableb VALUES(2,4);


UPDATE tablea
SET flag = tablea.flag | tableb.flag
FROM tableb
WHERE tablea.id = tableb.aid;


SELECT * from tablea;id | flag
----+------ 1 |    1 2 |    1

-- Desired output isid | flag
----+------ 1 |    7 2 |    5


Is there a way around this so that I can get the desired output?

-- 
David Stanaway <david@stanaway.net>