LAHORE -- A man in a small Pakistani town killed his Danish sister-in-law because he suspected her of having a "bad character", police Tuesday said.

Faisal Bashir shot dead 31-year-old Tahira Bibi, who was of Pakistani origin, local police official Mohammad Shahbaz Cheema told Agence France-Presse.

"It's a case of honor killing as Faisal suspected his brother's wife had bad character," Cheema said.

He added that police arrested Faisal, his two brothers and father after a complaint by the parents of Tahira, who settled in Kharian -- 150 kilometers (93 miles) northwest of Lahore -- after marrying Mohammad Shehbaz 10 years ago.

Her parents accused Shehbaz of asking his family to kill Tahira for not delivering him a baby boy.

"However, Faisal told us during interrogation that he shot dead his brother's wife in June after receiving numerous anonymous phone calls that she had a bad character," Cheema added.

He said the police had yet to complete investigations. "We are investigating the murder on scientific lines and hope to expose real culprits very soon."

More than 4,000 people, mostly women, have been killed in conservative rural areas of Pakistan in recent years in the name of protecting family honor.

In 2005 President Pervez Musharraf signed into law a bill introducing the death penalty for honor killings.