Jeremy Steinke, 26, was found guilty in 2008 of killing the girl's parents and brother two years earlier in Medicine Hat when she was 12 years old.
Steinke, who has changed his name to Jackson May, filed a notice of abandonment with the Alberta Court of Appeal in Calgary.
May is the last name of Steinke's mother Jacqueline.
Wearing a blue prison jumpsuit and with his hair freshly shaved into a mohawk, Steinke replied "Yes ma'am" when asked by the case management officer if he wished to give up his appeal.
Because he had filed the notice under his new moniker of Jackson May, he was also required to sign Jeremy Steinke to the paperwork to make it official.
Steinke had filed notice of his appeal too late and had the option of asking the court to extend his time. In his document he called the Dec. 5, 2008, decision by a Calgary jury "an unreasonable verdict."
He is serving three concurrent life sentences for first-degree murder with no chance of parole for 25 years. The victims were all stabbed to death.
Steinke's accomplice was also convicted of first-degree murder but because of her age received a 10-year youth sentence in closed custody and involving extensive rehabilitation. She is believed to be the youngest person ever charged with multiple counts of murder in Canada.
Now 18 and living in Calgary, she is reported to be making progress.
At her last sentence review in March, Justice Scott Brooker said she was taking post-secondary classes and had a job as part the Intensive Rehabilitative Custody and Supervision program.
He also said she had a "low probability of committing further acts of violence."
The Crown said she should continue to be supervised and wants the woman to reflect on her crimes and talk to therapists about what happened.
She began the fourth and final phase of her sentence last November. It will see her serve the last four years in the community.
The woman's next sentence review is tentatively scheduled for late September. She is to be fully released without supervision when she turns 22.
Court heard during the trials that the girl was angry with her parents because they were displeased with her relationship with Steinke. He was 23 at the time and her parents felt he was too old for their daughter.