Spectrally Efficient Frequency Division Multiplexing (SEFDM) system employs non-orthogonal multiple carriers in order to enhance utilization of bandwidth over the Orthogonal Frequency Division Multiplexing system (OFDM). However, the deliberate loss of orthogonality affects many aspects of the system. In particular, the intercarrier interference results in the system becoming ill-conditioned, thus affecting the performance of the system, and particular to this work, the channel estimation accuracy. Therefore, in this work, a novel channel estimation technique benefiting from the structure of the SEFDM system to tackle the ill-conditioning is tailored. The technique is termed Partial Channel Estimation (PCE) and is based on transmitting pilot symbols invoking the partial orthogonality structure of the system to avoid the ill-conditioning impact and thus, is capable of delivering more accurate estimates. Numerical performance of the proposed estimator confirms favorable estimation accuracy and demonstrates a tangible error performance improvement and complexity reduction.