In this paper, the controllability of diffusion coupled multi-agent systems under signed networks is studied. Firstly, the upper bound of the controllable subspace of the system is given based on the generalized almost equitable partition and the restriction on the coefficient matrix of the system. Compared with the previous similar conclusions, the influence of the choice of coefficient matrix on the conclusion is discussed and a necessary condition for the controllability of the system is given: All the cells in the partition are trivial when the system is controllable. Secondly, an algorithm for computing the leader-isolated maximal generalized almost equitable partition is presented. In addition, it is proved that the controllability of the general linear diffusion coupled multi-agent system is equivalent to the controllability of the corresponding all positive network if leaders are selected from the same vertex set under the condition of structural balance, but independent of the selection of system coefficient matrix.