Transferable of FD, it can be both Yes and No. It depends upon the situation.
Yes, you can transfer your fixed deposit accounts. However, you can only transfer your FD accounts from one branch of a bank to another branch of the same bank.
No, Transfer of fixed deposit from one bank to another bank, then it is currently not possible to do so. You would either have to wait till your FD matures or you would have to prematurely close your FD to invest the proceeds in another bank as a fixed deposit.