avalizing bank — авалирующий банк
It is then sent to the customer for acceptance and can be avalized (guaranteed) by the bank for additional safety. — Потом он [вексель\] отправляется покупателю для акцепта и, для большей надежности, может быть авалирован (гарантирован) банком.
To avalize means "to give one's accord". It is a rarely used but is an effective method of securing the rights of the receiving party in the transaction. This is an obligation that a bank will only take on with lucrative customers. It is seen as an act of good faith by both parties.