(CBSDFW.COM) – An execution date has been set for a Fort Worth man who was convicted in the 2005 murders of his pregnant ex-girlfriend and her 7-year-old son.

Stephen Barbee will be executed on October 2 by lethal injection, which is more than a decade after he was sentenced to death row.

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Stephen Barbee (Credit Texas Dept. Of Criminal Justice)

Lisa Underwood and her son, Jayden, were suffocated at their home in 2005 and then buried in Denton County, officials said.

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Prosecutors said Barbee killed Underwood because he thought she was pregnant with his child, and that he didn’t want his wife to know.

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A DNA test later determined that he was not the father of the unborn child.