The so-called Urewera Four are to appeal their convictions and sentences to the Supreme Court.
Tame Iti, Te Rangikaiwhiria Kemara, Urs Signer and Emily Bailey were all convicted of firearms charges following their trial in February.
The jury could not decide whether the four were part of a criminal group.
Iti and Kemara were both jailed for two-and-a-half years, while the other two were sentenced to home detention.
The Court of Appeal last month rejected their appeals.
But Kemara's lawyer Jeremy Bioletti says he will argue to the Supreme Court that the Crown's approach was contrary to the presumption of innocence.
Lawyers for the four will also argue the illegal gathering of evidence by the police should have been included as a mitigating factor in sentencing.
The appeals will be lodged before the end of the month.