I might also recommend using SBI Cal (if you’re not in a hurry that is and have time at hand).
Basically you start an account with SBI Cal, hook up your NRI account (assuming you already have it) and verify the process. Once done, you can deposit your money from any US account to SBI Cal and then transfer it online to your NRI account.
Why SBI Cal - I’ve found them to provide good exchange rates (again, if you’re not in a hurry). You can lock in on the sending day’s rate. The negative is that this whole verification process etc will take some time and you will not be able to send money immediately. Last time I used it, there was a 24 hour hold on your money before you can transfer. And their website isn’t the best to use.
But once done, there isn’t much of a loss as they offer food exchange rates.
I’m sure there must be some other better way, but as of now, this is what I know. Hope it helps.