What is the name of a security classification in the US that is higher than: Top Secrete and Black Ops?

[Gerri R]

For example, Navy Seals are a Government agency that is considered Top Secrete. In other words, we know they exist and we know some of the things they do. Such as getting Bin Ladden (At least that's what the government and news media tell us).

I am referring to what do they call a group that is even more classified than Navy Seals, CIA or even people who work at Area 51.
I was talking to a Marine, Force Recon, Sniper who served in Vietnam. His unit was considered Top Secrete. He couldn't tell me much, and even what little he did tell me scared him half to death. I'm not exaggerating when I say, he kept looking over his shoulder to make sure the Men In Black, as he called them, did not come over, arrest him and make him disappear off the face of the Earth!
But he said he worked with some guys while he was in the Marines that didn't even officially exist! When they signed up to do the job, their boss said, "Give me your Social Security card, drivers License, birth certificate, credit cards, voter registration and all other forms of I'D that you have." They put it all into a paper Shredder and burned them afterwords! Then he said, " You no longer exist. If you get taken prisoner by the enemy, I will say I don't know you! The Federal government will deny knowing you as well! Your name up until now was John Smith. Now you don't have a last name. Your new name is just: Tom. You have no military rank or anything, you just don't exist!
If someone asked him any unnecessary questions, they would be in serious trouble and might even be launched into space for ever!
When he worked with these people, the person introducing them don't even know anything about the other person. They just said, "This is Tom and that's all you and I need to know! You will be working with him for a few days or weeks. What you will be doing and where you will be going, I don't know and I don't need to know." When he came back from the mission, his Sergeants, commanding officers and everyone else wouldn't even dare ask him anything! Not where he went, what he did, who else went with him or even how long he was gone and when he came back. Because even they were too afraid to ask him a single question, because they feared for their own life if they asked any questions!

This is the security classification I'm asking about. What do they call this security classification? Higher than: Special Forces, Special Ops and Black Ops. What comes next?
This is the group's of people that they don't want anyone in the world to know anything about. They are even very reluctant to tell the President or the US Department of Defense anything about.

I am only interested in this because I am trying to write a book about a Top Secrete unit in the US Army that will be classified as way beyond Black Ops. So Secretive that they literally disappear from official resistance. The President, DOD, Army and even their own families won't even know that these people even still exist, nor will anyone know anything about their military unit which won't even have any official name at all.

(Basic plot summary: Several Special Forces soldiers go to Iraq. They sign up for a mission that is so dangerous and highly classified as way beyond Black Ops that no one can know anything about it and the soldiers have to officially die, before they start the mission. Their family is sent a death certificate and told "We're sorry, your Son, Father, Husband, etc has died and disappeared. We can't even find any of his remains. If it is any consolation, we are sending you one of his dog tags, which is all that is left of him." Then the adventure begins.