Due to the unprecedented growth of the Internet of Things (IoT), safeguarding IoT devices of wireless connection has now become more challenging than ever. As a new paradigm of security mechanisms, radio frequency fingerprint identification (RFFI) has attracted lots of research attention since it can be used to authenticate authorized users by exploiting the transmitter hardware characteristics. However, the channel variations will cause the distribution shift of the received signals and thus lead to an unreliable classification performance for RFFI in unknown channel environments. For this reason, this paper proposes a robust RFFI method to resist the unknown channel effects. Specifically, we first propose a signal preprocessing method named second-order spectral circular shift bidirectional division (SoSCSBD) to convert the received signals into the second-order spectral quotient (SoSQ) sequences, where the channel effects can be deeply suppressed. Secondly, considering the division-based algorithm will induce the outliers, we present the median absolute deviation aided outlier filter (MADAOF) to remove them so that the statistical stability of the filtered SoSQ sequences will be enhanced. Then, a low-dimension RFF extraction method using the principal component analysis (PCA) algorithm is proposed to construct feature samples with device-specific information. Finally, the feature samples collected under different channel conditions are sent to the multi-class support vector machine (SVM) classifiers for training and testing. Furthermore, we carry out extensive experiments to evaluate the performance of the proposed RFFI method. Numerical results suggest that the newly developed RFFI method exhibits strong generalization, achieving robust and superior performance in comparison to several existing methods under unknown multipath fading channels.