Starship, which consists of a booster and spacecraft, is being developed by Elon Musk's SpaceX. The businessman says the aim is to one day take humans to the Moon, Mars and beyond.
But the rocket has to complete a test flight to orbit before SpaceX can begin any kind of operations.
In April, Starship blew up mid-flight during the first orbital test flight, causing chunks of the rocket to tumble back to Earth after the launch from Texas.
Now, a new rocket, called Booster 9, has been test fired at Starbase, a facility in Boca Chica, Texas.
SpaceX shared footage of the static fire test – which involves firing the engines of the rocket and carrying out a countdown to mock a launch – on social media.
During the test, four of the rocket's Raptor engines shut down prematurely.
The first orbital test flight did not go as planned owing to a technical issue.
Starship had reached a peak altitude of 39km over the Gulf of Mexico when the mishap took place.
At the time, the company said that engineers had got “plenty of data” to try again. On the ground, SpaceX crew cheered the launch.
The cost of a single Starship has never been revealed, but Mr Musk said the broader project cost at least $3 billion.
According to SpaceX, Starship is the most powerful launch vehicle developed, capable of producing 3,991 tonnes of thrust – 15 per cent more than Nasa’s Apollo Moon rocket, Saturn V.
SpaceX is contracted by Nasa to develop the Starship Human Landing System, which is aimed to help astronauts land on the Moon under the US space agency’s Artemis programme.
Mr Musk has already sold seats on the Starship, including to Japanese billionaire Yusaku Maezawa, who plans on flying on the first crewed flight to the Moon, taking eight artists with him as part of his dearMoon programme.
American billionaire Jared Isaacman is also working with SpaceX through his Polaris programme, a series of privately-led space missions.
Mr Isaacman will serve as commander on the Polaris III mission – the first crewed orbital flight on the Starship rocket.