Monogamy of entanglement is an important property in quantum entanglement, which can be used to characterize the entanglement structure in multipartite systems. Tsallis-q entropy entanglement is a well-known entanglement measure and the squared Tsallis-q entropy entanglement obeys a monogamy relation. The entanglement monogamy relation satisfied by the μ-th power of squared Tsallis-q entropy entanglement for μ2 has been proved by Yuan etal, and a new monogamy relationship for squared Tsallis-q entropy entanglement is presented here, which is tighter than that have been proven previously.