Condition monitoring of BLDC motors due to their important applications is gaining more and more significance. Rotor eccentricity is one of the most important sources of faults in these motors. Up to now, detection methods of this fault under nonstationary conditions are limited to complicated and time-consuming methods using wavelets and Cohen class algorithms which are difficult to implement and need heavy computations to run. In this paper a novel method based on the modified Motor Current Signature Analysis method is proposed to detect the rotor eccentricity fault of BLDC motor operating under varying speed conditions. Stator current of healthy and faulty motor which are modeled by the Finite Element Method are simulated. By changing the representation of stator current from time basis to angle basis, the current signal will become stationary. Thus there is no need for methods using time-frequency analysis. Afterwards the Order Analysis Method is applied to the simulated healthy and faulty angle-based current signal and the results are compared with each other. Finally, the fault is detected by this comparison.