In the study, the finite-time synchronization (FTSN) for a kind of master-slave quaternion-valued fractional-order neural networks (MSQVFONNS) is discussed. By using the negative definition of matrix and the properties of the determinant, two novel criteria on the FTSN for the considered MSFOQVNNS are established. The negative definition of the matrix and the properties of the determinant are introduced to study the FTSN for neural networks (NNs) in our article. Since until, studies about the FTSN for the NNs are rare and researchers have only used the linear matrix inequality (LMI), finite time stability theorems (FTSTs) of fractional order and Lyapunov direct method to study the FTSN for the MSFOQVNNS, so far, our method to study the FTSN for the MSFOQVNNS is of definite significance.