Work to knock down the building in George Street started in April.
The blaze broke out at the former amusement arcade and nightclub on January 18.
Firefighters were called to the scene just after 7.15pm, with up to 10 pumps spending all night tackling the blaze. Residents in nearby properties also had to be evacuated.
Firefighters were still at the scene early the next morning and the road had to be closed off to traffic until later that day.
On January 30, Sussex Police said the fire was being treated as ‘deliberate ignition’.
The road where the amusement arcade was remained closed off until demolition work was completed.
The Rainbow Restaurant, in Sturdee Place, suffered extensive damage as a result of January’s fire.
On its Facebook page, its owners said on January 27 that they will not be able to open the restaurant for ‘at least six months’.
The three-storey building in George Street used to operate as an amusement arcade and once housed a nightclub.
The building was sold for redevelopment into 20 flats in November last year. Planning permission was then sought to demolish the building to make way for four commercial units and 21 flats. But the application has since been withdrawn.
Firefighters were called to the scene just after 7.15pm, with up to 10 pumps spending all night tackling the blaze. Residents in nearby properties also had to be evacuated.