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In this letter, we consider the secure network coding problem with no restriction on the network coding vectors. Adeli and Liu proposed a scheme achieving perfect security in a network with network coding. In order to hide a security weakness of their scheme, they imposed a restriction on the linear network code design. However, this restriction can be violated when the random linear network coding is used due to the completely decentralized nature of it. We refine Adeli and Liu's scheme into new one with no restriction and thus remove the security weakness under the computationally bounded adversary assumption.