Making Internet Banking More Secure

Recently someone tried to reset my net banking password. I called the bank but they were not even aware of it.

They told me they would check but no response.

All banks really want their customers to use net banking, its convenient for them and their customers. But not really secure.

Now i thought was there a way to make me more confident of using net banking.

I wish for users who have provided a email or mobile number, they would send a mail and a sms when their is any activity related to their account online or even offline. When this happens they could let the user respond via sms or click on a link in their email, when a customer does this, the user who is trying to access their account online is banned from accessing the site for sometime.

Seems like a logical thing to do to me. And when it comes to banking its required.