Diagnosis technique of bearing failure in a rotating machine is very important for industry. There are a lot of researches and some practical diagnosis methods are applied in actual industrial systems. In the paper, problems of conventional diagnosis methods for the case of low-speed rotation are explained, a new diagnosis method for rolling bearings is proposed, and its principle is explained in detail. In the conventional diagnosis method, piezoelectric acceleration sensors are usually used to detect abnormal vibration signal of bearing during rotation. In the paper, a jerk sensor which is originally developed by the author is used for the proposed diagnosis method. When a failure such as flaking exists on outer or inner ring surface of the rolling bearing, impulse-like vibrations occur whenever each roller passes over the flaw. The period of the pulse-like vibration is called pass flaw period (PFP) in this paper. Both of the conventional and proposed methods diagnose bearing failure by detecting whether impulse-like vibrations which occur with the same period as the PFP, or not. However it is very difficult for conventional methods to diagnose a bearing rotating at low speed. Basic idea of the proposed method is similar to AND of bit-operation in digital signal processing. Multiplication among vibration waveforms divided by PFP is taken. The multiplication signalizes only the impulse-like vibration synchronized with the PFP. Effectiveness of the proposed method is verified using a test bearing with a scratch as simulated flaw for rotation speed of 40 and 10rpm.