The “second negative” is also called the “double negative.” Don’t confuse it with the “negative double” – they are totally different bids.
Partner opens 2♣
When partner opens 2♣ and you have a crummy hand, you first respond 2♦. This is just a negative bid, showing 0 to 7 points. But if you are truly dreadful, you need to turn partner off from his lofty dreams by giving him a “second negative.”
This is an important convention that comes in handy.
Responder’s Second Bid
Modern bidding has a problem-child:
♠ Q 8 7 North South
♥ A Q 9 8 7 1♦ 1♥
♦ K J 6 1♠ ??
♣ 5 4
South has a problem: He wants to bid NT, but not without a stopper in clubs, the only unbid suit. He should not jump in his 5-card heart suit (only perverts do that), and he should not raise opener’s second suit with only 3-card support. There is a nice solution to this dilemma: