OFDM based pilots channel estimation methods with processing into the transform domain appear attractive owing to their capacity to highly reduce the noise component effect. However, in current OFDM systems, null subcarriers are placed at the edge of the spectrum in order to assure isolation from interfering signals in neighboring frequency bands; and the presence of these null carriers may lead, if not taken into account, to serious degradation of the estimated channel responses due to the “border effect” phenomenon. In this paper an improved algorithm based on truncated SVD is proposed in order to correctly support the case of null carriers at border spectrum. A method for optimizing the truncation threshold whatever the system parameters is also proposed. To make the truncated SVD channel estimation method applicable to any SISO or MIMO OFDM system and whatever the system parameters, a complexity reduction algorithm based on the distribution of the power in the transfer matrix (based on DFT or DCT) is proposed.