I have a friend who is married to an immigrant in the us for 5 years I think! And they had a son who is a us citizen by birth.my friend is not yet petition since the wife have to finish her study first.but then when the wife finished her study flew to America and already work there. The problem is no communication for almost a year. And I was thinking if the wife could be married again in the US though she is married in another country where she is born?is there a way to registered the marriage so that the wife could not marry again without further annulment/arrangement with the husband?thank you.:)

No, she could lie and get married, but the marriage would not be legal if someone showed where she was still married.

There is not even national records of marriage from one state in the US to another,

The second marriage is illegal and not valid but it would have to be reported

Yeah your right she can lie about her status what I'm thinking and what to advice to a friend of mine is to ask the embassy about it and registered their marriage is there such thing?

No, there is no such place in the U.S. The only registration that goes on is at the local level. ( the city or county the marriage license came from ) and that's about it.