Update rows when in other table

I have two tables TAB_A and TAB_B. I want to update COL_1 in TAB_A to a certain value but only for rows where the value COL_2 in TAB_A is also found in COL_2 of TAB_B.

This is what I have but it seems to then set COL_1 of TAB_A to a NULL if its not found in TAB_B. In this case I just want to leave that row unchanged.

UPDATE tab_a
SET col_1 = 'NEWVALUE'
WHERE EXISTS (SELECT 1

                                FROM tab_a a, tab_b b
                                WHERE a.col_2 = b.col_2)
                                AND col_1 IS NULL;

Any ideas to what I'm doing wrong?

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Cheers,

elziko