He also recommended that public interest cases be heard by a seven-member panel while other appeal cases should be heard by a five-member panel.
Malanjum, who was sworn in as the Chief Justice yesterday, said applications for leave to appeal should be heard by a three-member panel and the members should be selected through balloting.
"We like to do this in a sense I don't have to crack my head (on) who to sit (on the panel). We go by balloting.
"Appeal cases originated from Sabah and Sarawak should be heard by a panel consisting of at least one judge from these states," he said in his maiden speech at the swearing in of the Court of Appeal president and the Chief Judge of Sabah and Sarawak.
Tan Sri Ahmad Maarop was sworn in as the Court of Appeal president while Datuk David Wong Dak Wah was sworn in as the Chief Judge of Sabah and Sarawak.
Currently, the Federal Court panel which hears appeal cases and review applications comprises five judges while the panel which hears the applications for leave to appeal comprises three judges.
Malanjum said a number of new approaches would be implemented including a joint and group management concept where the top four judges would be given the same power and responsibilities in all matters relating to policies and participation in the management of the judiciary.
"The Federal Court, Court of Appeal and High Court will be led by senior judges in accordance with the role as provided in the Federal Constitution.
"The judges will be responsible for managing their respective courts," he said.
He also suggested that a time-sheet system be introduced in the High Court to ensure judges were not accused of playing truant.
Malanjum said he had introduced the computerised system two years ago in Sabah and Sarawak courts.