This paper analyses the disturbance error coefficients for the active disturbance rejection control(ADRC) system and proposes a new method to improve the disturbance rejection performance using the m-th order extended state observer(ESO) in order to guarantee the high-precision stabilisation performance of control systems. Using the first order extended state observer in the ADRC system, the disturbance rejection performance is limited due to the disturbance error coefficients. As well, the m-th order extended state observer was hardly used for the active disturbance rejection control. In this paper the relationship between error coefficients and gain coefficients of observer and the relationship between error coefficients and natural angular frequency of observer of the ADRC system are analysed for the plant representing in the canonical form according to the extended state order m, and the disturbance rejection performance on the constant, ramp, parabolic and harmonic disturbances is analysed comparing with the results in [32]. The proposed method shows that the constant, ramp and parabolic disturbances are rejected perfectly according to the increase of extended state order m while the rejection performance is improved for the harmonic disturbance of the same frequency by the multiple of m. Taking the merits of principle and method of ADRC and introducing the m-th order ESO the disturbance rejection performance can be improved by making the error coefficients to be ‘zero’ according to the extended state order m.