The frequency domain pilot multiplexing technique (FDPMT) for channel estimation prevails in single-carrier frequency domain equalization (SC-FDE) systems for high spectral efficiency it promises. However, the bit error rate (BER) performance of the system with FDPMT can be significantly affected by the signal distortion level, which depends on the signal reconstruction (SR) ability of the receiver. In this paper, we are the first to discover that the time domain distortion block due to the removal of several equal-spaced data tones is comprised of an equal number of independent distortion sub-blocks. Motivated by this property, we therefore propose a novel SR method based on the maximum-likelihood (ML) criterion. It can be carried out sub-block-by-sub-block in parallel and sample-by-sample within each sub-block, keeping similar computational complexity to the existing SR method. More importantly, it gets rid of the error propagation problem that is encountered in the existing SR method, thus exhibiting much better BER performance over time-varying Rayleigh fading channels.