Based on the block bordered diagonal matrix structure， this paper presents a new discrete decomposition algorithm for the reactive-power optimization in a multi-area power system. The method decomposes a power system into several sub-areas according to certain rules， and establishes border networks between the sub-areas by introducing fictitious buses. The nonlinear primal-dual interior-point algorithm and discretization penalty method are used to solve the problem. As a result， the coefficient matrix of the linear correction equation has a block bordered diagonal structure. To search the quasi-optimal discrete solutions for the whole system and sub-areas， two decomposition methods are proposed to solve the linear correction equation of each sub-area independently. The results on IEEE 118-bus test system and two practical systems， 538 buses and 1133 buses respectively， validate the effectiveness of the proposed algorithm in comparison with the centralized optimization method.