The existing subspace-based channel estimation approach for orthogonal frequency division multiplexing (OFDM) systems with an expanding factor, called the repetition index, suffers from the problem of low probability of full row rank of the signal matrix with few OFDM blocks, which may fail to estimate the channel impulse response (CIR). In this paper, a subspace-based channel estimation algorithm with a two-step signal matrix construction method is proposed. The probability of full row rank of the proposed signal matrix is very close to one even if few OFDM blocks are available. The proposed approach can also be applied to both cyclic prefix (CP)-based and non-CP-based OFDM systems whereas the conventional approach is only suitable for CP-based systems. Simulation results show that the proposed method outperforms related blind channel estimation approaches in terms of normalized mean square error (NMSE).