The recording of auditory brainstem response (ABR) at high stimulation rates is of great interest in audiology. It allows a more accurate diagnosis of certain pathologies at an early stage and the study of different mechanisms of adaptation. This paper proposes a methodology, which we will refer to as randomized stimulation and averaging (RSA) that allows the recording of ABR at high stimulation rates using jittered stimuli. The proposed method has been compared with quasi-periodic sequence deconvolution (QSD) and conventional (CONV) stimulation methodologies. Experimental results show that RSA provides a quality in ABR recordings similar to that of QSD and CONV. Compared with CONV, RSA presents the advantage of being able to record ABR at rates higher than 100 Hz. Compared with QSD, the formulation of RSA is simpler and allows more flexibility on the design of the pseudorandom sequence. The feasibility of the RSA methodology is validated by an analysis of the morphology, amplitudes, and latencies of the most important waves in ABR recorded at high stimulation rates from eight normal hearing subjects.