BEIJING, April 6 (Reuters) - Xiamen Air has started technical modification on its grounded Boeing 737 MAX planes, the all-Boeing carrier said on Tuesday, although it said it does not have a timetable for the jet's return to service in China.

China is one of the last major markets to hold out on clearing the 737 MAX and an increasing headache for Boeing which replies on China for about a quarter of sales.

"Boeing has recently issued some technical guidelines regarding the MAX. According to these guidelines, we have started on the modification, which is a necessary step towards the return to service (of MAX)," Xiamen Airlines, a subsidiary of China Southern Airlines, said in a statement to Reuters.

"However, currently we do not have a timetable for its return to service and everything is subject to notices from the aviation regulator."

China was the first country to ground the 737 MAX in March 2019 following two fatal crashes which killed 346 people. At the time, more of the planes were operating in China than anywhere else.

The Civil Aviation Administration of China (CAAC) said in March that it was studying a plan with the U.S. planemaker for clearing the aircraft to fly in China.

Three principles outlined by the CAAC include certified design changes, proper training for pilots and specific findings into the crashes.

The U.S. Federal Aviation Administration (FAA) lifted its flight ban on the 737 MAX in January. It was followed by the European Union Aviation Safety Agency (EASA) and several others.

Vietnam on Tuesday lifted a ban on transit by 737 MAX planes.

(Reporting by Stella Qiu and Tony Munroe in Beijing; Additional reporting by Jamie Freed in Sydney and Tim Hepher in Paris; editing by Jason Neely)