There were four Rimmer brothers: John, Howard, Frank and Arnold. Their father was obsessed with getting them into the Space Corps and continually tested and cajoled his sons to that end, making their meals contingent on passing enrollment questions. To ensure they met the height requirements, Mr. Rimmer used a traction table to stretch his sons. ("Better Than Life").
The three older brothers bullied Arnold fiercely, although he rationalized it as playful high-jinks. Even when they placed a landmine in his sandpit, he laughed it off. During their "Three Musketeers" game, Arnold always had to play the Queen of Spain ("Polymorph").
Howard later joined the Space Corps Super Infinity Fleet.
Arnold and the rest of the Red Dwarf crew eventually rescue Howard's hologram from the Columbus 3, the ship he was serving on, which had been attacked by a killer Simulant. Arnold pretends that he is a Space Corps big-shot and the Captain of the then derelict SS Trojan, prompting his brother to confess that he himself is not actually a big-shot at all; he is in fact a vending machine repair man (presumably technician level), just like Arnold. He later sacrifices his life to save his brother from the same Simulant that destroyed his ship, prompting the JMC on-board computer to posthumously award him the Platinum Star of Fortitude, the Space Corps highest military decoration. It even suggested that the Red Dwarf be renamed the "SS Howard Rimmer" in his honour, driving Arnold into another resentment overload. ("Trojan").
Behind the scenes
In a deleted scene from "Rimmerworld", Kryten revealed that all three of Arnold's brothers became highly decorated officers, but all went insane and in some way killed their crews. Arnold was rather touchy on the subject.
In the booklet accompanying the DVD of Series III, it was suggested that Howard and his brothers were actually the sons of the man they called Uncle Frank. Either way, they would actually be Arnold's half-brothers, as it is revealed in "The Beginning" that his real father was the family gardener "Dungo" Dennis; how similar Howard turned like Arnold however may perhaps suggest that he is Dungo's child too.