Paralyzed U.S. Olympian -- 'Getting Better Every Day' ... Moving Arm! (VIDEO)

The former Team USA Olympic high jumper who was paralyzed in a training accident in California last month says he's making HUGE progress -- and can now move his arm!!!

As we previously reported, 2-time Olympic high jumper Jamie Nieto fell on his head while training Olympic hopefuls last month ... and suffered major damage to his spinal cord.

But in a new video shot from his hospital bed, the 39-year-old said he's "getting better every day. Just feeling a lot better."

Nieto -- who underwent emergency surgery following the life-threatening accident -- is also trying to walk again ... though it might take some time.

"It's been a tough experience, not easy. You know, learning how to walk again, move my hands and getting my feet moving again."

"But I'm getting stronger, so it's getting better. It's a process. I thank everybody out there for all their love and support."

Nieto's girlfriend has said he's a fighter who hopes to be jumping again as soon as possible.