The repatriation process was stalled for more than 16 months and only last week the dates for its resumption were finalized.
At least 21,000 Rohingya refugees are now camped in two shelters in Cox’s Bazar, and Burma has so far agreed to take back only seven thousand of them.
About 250,000 Muslims fled to Bangladesh in 1991, accusing Burma’s military, which is predominantly Buddhist, of systematic murder, rape and forced unpaid labor.
The preparations for the resumption of the repatriations were taken amid heavy secrecy.
The Bangladesh Government began the process of returning about 7,000 Rohingya refugees returned to Burma on Wednesday.
A group of 46, which included women and children, was accompanied by local representatives of the United Nations High Commissioner for Refugees and the Bangladesh government.
The refugees were met by Burmese immigration officials.
Officials in Cox’s Bazar in Bangladesh say the next batch of refugees will be repatriated next Wednesday.
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Sources say the Bangladesh government is negotiating with Burma to increase the number of refugees to be repatriated in a day and also to carry out the operation at least three times a week.
A BBC Correspondent in Dhaka, Kamal Ahmed, says the caution was understandable given the number of complications that have bedevilled the return of the refugees for nearly 16 months.
As recently as 13 November when he returned from Burma, the Bangladeshi Foreign Minister, Abdus Samad Azad, said that no firm date had been agreed.
Analysts in Bangladesh say the return of the refugees is a sign of the effort Bangladesh has made to forge closer economic ties with Burma.
In recent months the two countries have signed deals on border trade, a demarcation treaty on their joint border and an agreement to establish a new regional economic forum, Bimstec, with India, Sri Lanka and Thailand.