I asked a question and got this reply which helped.
UPDATE TABLE_A a JOIN TABLE_B b ON a.join_col = b.join_col AND a.column_a = b.column_b SET a.c
For PostgreSQL example:
UPDATE TableA AS a SET param_from_table_a=FALSE -- param FROM TableA FROM TableB AS b WHERE b.id=a.param_id AND a.amount <> 0;