Rolling element bearing signals are known to exhibit pseudo-cyclostationary properties that limit the efficiency of health monitoring. This paper investigates the restoration of cyclostationarity of train of impulses generated by bearing faults with the definition of a bearing angle-time relationship. Two main contributions structure the present paper. The first part presents a unifying synthesis of the state of art on the issue. The concept of cycle of reference (CoR) for cyclostationarity is presented. The possible causes of the well-used concept of slippage of the rolling-element bearing are explored to highlight the limitations of the cyclostationary theoretical framework. The influence of different types of jitters is presented to show the effect of using shaft cycle of reference on the spectral properties. CoR, on which bearing signals are phase locked so to restore their cyclostationarity, and a method to estimate the appropriate angle-time relationship are introduced. In a second part, original contributions on demodulation parameters and the possible introduction of unwanted artefacts are thoroughly explained along with the definition of a hypothesis test. The superiority of cyclostationarity restoration for monitoring purposes is illustrated on two industrial cases.