When prior knowledge is available, it is beneficial to use constrained blind source separation (BSS) algorithms that can utilize more information to distinguish the desired source from artifacts and noise. This paper proposes a one-unit second-order blind identification with reference (SOBI-R) algorithm for short transient signal extraction, which reformulates the conventional second-order blind identification (SOBI) algorithm in an iterative manner to achieve joint diagonalization and the reference information incorporated. The proposed algorithm was applied to single trial extraction of somatosensory evoked potential (SEP). The experimental results demonstrated its effectiveness. Compared with other algorithms including the autoregressive model with exogenous input (ARX), artificial neural networks (ANN) and one-unit the independent component analysis with reference (ICA-R), the proposed SOBI-R algorithm shows high robustness under conditions with low signal-to-noise ratios and less sensitivity to the reference signal.