A user who does not have a quantum computer but wants to perform quantum computations may delegate his computation to a quantum cloud server. In order that the delegation works, it must be assured that no evil server can obtain any important information on the computation. The blind protocol was proposed as a way for the user to protect his information from the unauthorized actions of the server. Among the blind protocols proposed thus far, a protocol with two servers sharing entanglement, while it does not require to a user any quantum resource, does not allow the servers to communicate even after the computation. In this paper, we propose a protocol, by extend this two-server protocol to multiple servers, which remains secure even if some servers communicate with each other after the computation. Dummy gates and a circuit modeled after brickwork states play a crucial role in the new protocol.