This paper presents a blind identification algorithm for single-input single-output (SISO) plants using an oversampling technique with each input symbol lasting for several sampling periods. First, a state-space equation of the multi-rate sampled plant is given and its associated single-input multi-output (SIMO) autoregressive moving average (ARMA) model is formulated. A new blind identification algorithm for the SIMO ARMA model is then presented, which exploits the dynamical autoregressive information of the model contained in the autocorrelation matrices of the system outputs but does not require the block Toeplitz structure of the channel convolution matrix used by classical subspace methods. A method for recovering the transfer function of the SISO system from its associated SIMO transfer functions is further given based on the polyphase interpretation of multi-rate systems. Finally, the effectiveness of the proposed algorithm is demonstrated by simulation results.