An attack on an Orange Hall near Maghera was the second in 10 days, the Orange Order has said.
Scorch damage was caused to Killygullib Orange Hall hall during a petrol bomb attack at about midnight on Friday.
An Order spokesman said the attack was "mindless hooliganism" and 10 days earlier paint was thrown at the hall.
"The attack on the hall wasn't just aimed at Orangemen, it was an attack on an entire community in an isolated and poorly served rural area," he said.
"Those responsible should be truly ashamed of themselves and we urge anyone who might be able to help identify them to contact the police as soon as possible."
He said the County Londonderry hall had only been rebuilt two years ago after being badly damaged by vandals and was used by a playgroup, several church missions and other social groups.
Officers attacked
Police said they were investigating a possible link with the attack on the hall and an incident when officers were attacked with bottles and bricks while protecting the occupants of a broken down van.
Several cars stopped and blocked the van's way and the men inside fled during the incident on the Moneysharvan Road in Maghera at about midnight.
When a crowd gathered, police attempted to clear the road and seized a number of items, including sticks.
A police car was damaged during the incident on the Moneysharvan Road as officers were attempting to get the occupants of the van to safety.
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