According to APRA, the following banks have consent to maintain a representative office in Australia that are not authorized deposit taking insitutions
Banco Bilbao Vizcaya Argentaria S.A.Bank of Valletta p.l.cChina CITIC Bank Corporation LimitedCommerzbank AGCredit Industriel et CommercialCTBC Bank Co., Ltd.DOHA Bank Q.S.C. Global IME Bank LimitedIntesa Sanpaolo S.p.ANational Bank of Greece SAPunjab National BankSvenska Handelsbanken AB The Bank of Nova ScotiaThe Korea Development Bank The People's Bank of ChinaWells Fargo Bank, National AssociationSource: http://www.apra.gov.au/adi/Pages/what-is-a-representative-office.aspx