Blue Origin conducted the test on Monday in West Texas but released the video Tuesday morning.
The company said the rocket, with a crew capsule, reached a height of 62 miles, and in just a few minutes, the capsule made a controlled vertical landing from where it took off.
The test proved the possibility of reusing rockets, which could save commercial aeronautics a lot of money.
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Musk tweeted Bezos and the Blue Origin team for achieving take-off and landing on their booster.
However, the SpaceX owner also took a dig at Bezos to clear up the difference between space and orbit.