Three members of a Montreal family convicted of the so-called honour killings of four relatives will have their appeal heard in a Toronto court today.

Mohammad Shafia, his wife Tooba Yahya and their son Hamed Shafia were found guilty in January 2012 of first-degree murder of three sisters and Shafia's first wife in a polygamous marriage.

One of the arguments to be brought in front of the Court of Appeal for Ontario is that the trial judge was wrong to admit evidence from an expert on honour killings and a new trial is sought.

The bodies of Zainab, 19, Sahar, 17, and Geeti, 13, Shafia as well as Rona Amir Mohammad, 52, were found June 30, 2009 in a car submerged in a canal in Kingston, Ont.

The Crown's theory was that Shafia, Yahya and Hamed drowned the four victims elsewhere on the site, placed their bodies in the car, then pushed it into the canal with the family's other vehicle.

The defence argued it was an accident, that they had gone for a joy ride with one of the sisters driving and accidentally plunged into the canal.

The trio have maintained their innocence.

Following the guilty verdict, Judge Robert Maranger described the crime as "cold-blooded, shameful murders" resulting from a "twisted concept of honour."

The Shafia family is not expected to be in court Thursday.

-With a file from Gloria Henriquez