If you ask avowedly Orthodox Rabbi Arele Harel what he thinks about marriage between homosexuals, you may be surprised by his answer. Not only is he in favour, but he will play matchmaker.

However, there is a twist. The marriages that he brokers are indeed between gays - but one gay man and one lesbian. Couples then live in Orthodox communities, and nobody is the wiser about their unconventional relationships.

Rabbi Harel, a teacher in the Elon Moreh Yeshiva in the West Bank, has been making this kind of match for six years, notching up 13 couples. Now, Kamoha, a non-profit body representing gay Orthodox men, has decided to popularise it, opening a matchmaking agency that Rabbi Harel oversees.

The website for the agency, Anachnu (which means "us"), went live a fortnight ago and Kamoha's leader, Amit, said that it has already prompted dozens of enquiries.

Amit, who will not reveal his full name because he is in the closet, said that while some secular gays consider it a step backwards, this is actually a progressive solution. "Instead of marrying a woman and not telling her, all the cards are on the table," he said.

Registration costs 150 shekels (£25), and if people fund a match they pay a further 1,500 shekels (£250). Anachnu strongly suggest that couples consult counsellors to help figure out how their relationship will work, but leaves all details to the couple to decide.

Amit stressed that the marriages are not an attempt to change people's sexual orientation - they are actually only open to people who are certain that they are gay - and that they are only for people who like the idea. He said: "We are not saying that all gays should marry a woman - absolutely not."