Summary: The direct torque control on brushless DC motor is a newly issue. However, there are two deficiencies in existing scheme. Firstly, the stator flux-linkage reference is the function of rotor position; secondly, the variable voltage of turn-off phase make it difficult to calculate stator flux-linkage. These two deficiencies complicate the control system and the essential reason is the present of turn-off phase. For solving these problems, the turn-off phase is analyzed thoroughly and an conclusion is presented. The turn-off phase affects the stator flux-linkage, but had nothing to do with the torque. Then, the hyperspace vector theory for brushless DC motor is brought forward. The turn-off phase voltage is put along the \(Z\) axis perpendicular to the abc plane. The voltage vector and stator flux-linkage vector move in three dimensional space. The projection locus of stator flux-linkage is hexagon which is the integral of two conduction phase voltages. The turn-off voltage is ignored in realization system as its zero projection on the abc plane. The direct self-control is adopted, and the rotor position is unnecessary. The theory greatly simplifies the system. Simulation and experimental results validate the theory.