(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.

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.

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

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