If this situation is familiar, then it is time to talk to your lender. However, as has been mentioned earlier, your repayment track record has to be spotless. Your first request should be to ask him to charge you the same rate that the bank is charging their new customers. However, some lenders might charge a small fee for shifting your loan to a lower rate.
If your lender seems reluctant in taking this step, then you can certainly consider the other option of shifting the home loan to another lender offering lesser rates. And you can let your existing lender know that!
However, this step would give you a certain troubles. There would be certain fees to take care of, e.g., prepayment fee payable to existing lender and processing fee payable to new lender, besides administrative costs. Also, you would be required to furnish a NOC from the society or builder, whichever is applicable in your case, on payment of a fee.
The final thing left would be to procure a letter from your existing lender to the new one. You would be required to furnish that letter from your existing lender stating that they will release the documents within a stipulated time frame after full payment is made and also specifying the amount that will be required as full and final payment. This letter will enable the new lender to consider releasing the payment directly to your existing lender.
Hence, by one way or the other, you can change your floating rate of interest to a lesser value, easing the pressure on your pocket. So, go on, and talk to your lender today itself. All the best.