It is narrated from Nafi' that Ibn Umar (may Allah be pleased with them both) informed him that Rubayyi' bint Mu'awwidh bin Afra' (may Allah be pleased with her) took khul' from her husband in the time of Uthman (may Allah be pleased with him). Her paternal uncle, Mu'adh bin Afra' (may Allah be pleased with him), went to Uthman (may Allah be pleased with him) and said: The daughter of Mu'awwidh has taken khul' from her husband today; may she move out? Uthman (may Allah be pleased with him) said: She may move out, and there is no waiting period ('iddah) upon her, but she must not marry until she has passed one menstrual cycle. Abdullah bin Umar (may Allah be pleased with them both) said: Uthman (may Allah be pleased with him) is the eldest of us and the most knowledgeable of us. This narration makes clear that it was Uthman (may Allah be pleased with him) who ordered her to do that, while the apparent meaning of the Book concerning the waiting period of divorced women covers the woman who takes khul' and others, so it is more appropriate; success is from Allah, and Allah knows best.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب العدد / 15601