Can a committee member who has acted without committee discussion and agreement be voted off the committee?

a member of the committee has ordered decoration work and other tasks to be undertaken by independent trades people without consulting with the rest of the committee. The chairperson and other members are getting totally frustrated with this behaviour. Also the member in question is not designated as a key-holder to the premises but seems to be in possession of a key nonetheless. There is doubt as to whether a vote can be taken by the rest of the committee to expel this member from the committee. It is not known whether a constitution was ever agreed with the original committee. The present committee is mostly comprised of totally new members and the existing members are not aware of there being a written constitution. I would also be grateful if anyone can advise me on how a committee should be set up.