ASB has cut its 3 month term deposit rate by 10 basis points to 4.90% and has cut its regular 6 month deposit rate by 20 basis points to 5.00%.
This followed the Reserve Bank's dovish monetary policy statement last week which triggered a move lower in wholesale interest rates.
ASB has also introduced a new special 6 month term deposit rate at 5.30%.
This is slightly above the other major banks, but below Rabobank's BankaRate deposit rate on 5.5%.
Meanwhile, RaboDirect said it was dropping its three month term deposit rate to 4.85% from 5%, but lifting its six month rate to 5.15% from 5.05% and its nine month rate to 5.20% from 5.15%.
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(Update adds RaboDirect changes).