Delete using a composite key
Should be something like this:

DELETE A
FROM 
    table_example1 AS A
    INNER JOIN table_example2 AS B
    ON A.COLUMN1 =B.COLUMN1
    AND A.COLUMN2 = B.COLUMN2
WHERE
    COLUMN_DATETIME &gt; @Period;


Alternatively:

DELETE FROM A
FROM dbo.table_example1 AS A
WHERE EXISTS
(
    SELECT *
    FROM dbo.table_example2 AS B
    WHERE
        B.COLUMN1 = A.COLUMN1
        AND B.COLUMN2 = A.COLUMN2
        AND B.COLUMN_DATETIME &gt; @Period
);