The accused later went to the police station and surrendered, police said.
After the accused confessed to killing his sister-in-law, police reached his house where the woman's body was found lying on the terrace, they added.
Her husband and children were sleeping in a room unaware of what had happened.
The victim, a mother of four, used to stay with her in- laws and husband in Mukundpur area. In the wee hours on April 16, when the family members were asleep, the accused woke her up.
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He picked up an argument with her and confronted her with the allegations, police said.
He lost his temper during the argument and strangulated the woman with her dupatta and left the body on the terrace.
Police said the accused had surrendered and narrated the entire incident.
He told them that the woman was in a relationship with another man. He also said that a few days before her murder, he had broken her cellphone following an argument on the same issue.