How do i go about matching three fields from two tables in order to update the same tables in case of match

Question

Given two tables A and B in a MySQL Database, how can one update a field in a row of table A if and only if certain fields in the fore-mentioned row in table A exactly match fields in a distinct row of table B. The rows in table B must be used once and only once for each comparison. As such, a row in Table B that has fields matching a row in Table A can not be used a gain to match any other row in Table A.

I have tried

UPDATE
    Table A,
    Table B
SET 
    Table A.Status = 'MATCHED',
        Table B.Status = 'USED'
WHERE
    Table B.Status IS NULL
AND 
    Table A.Field1 = Table B.Field1
AND 
    Table A.Field2 = Table B.Field2

Unfortunately, this does not give my desired results since different rows from Table A tend to get matched with the same row in Table B.

For example: Table A

ID  Date       Ref    Amount  Status 
1   2009-10-20 773    300000         
2   2009-10-20 773    10000   MATCHED
3   2009-10-20 773    150000         
4   2009-10-20 773    20000   MATCHED
5   2009-10-20 773    140000  MATCHED

Table B

 Ref Amount Date       ID
 870 50000  2009-11-01 1 
 871 50000  2009-11-01 2 
 871 80000  2009-11-01 3 
 871 20000  2009-11-01 4 
 871 20000  2009-11-01 5 
 871 20000  2009-11-01 6 
 872 300000 2009-11-01 7

To match using Ref, Amount and Date.

Answer 1

Add more conditions to your WHERE clause to force a 1:1 match between records in tableA and tableB?

Answer 2

Could it be as simple as adding exclusions to the WHERE clause to avoid reuse?

AND Table A.Status <> 'MATCHED'
AND Table B.Status <> 'USED'

This will work if each row is updated in turn, but not if it's set based and transactional. My apologies for not testing this; I don't have MySQL here to try this with.