Achieving high speed in decision feedback equalizers (DFE's) is difficult because of the nonlinear decision directed adaptation. Recently, parallel DFE and extended LMS DFE algorithms were proposed for parallel implementation of DFE's. In this correspondence, we first present a new double-row DFE algorithm which outperforms the previous approaches. Under the no error propagation assumption, our algorithm will perform exactly like a serially adapting DFE. The multiplication complexity of the double-row DFE algorithm is of the same order as the parallel DFE algorithm and the extended LMS method. The previous algorithms and the double-row DFE algorithm may become impractical to implement due to their large computational complexity. We propose three additional novel parallel implementations of the DFE which lead to considerable hardware savings and avoid the coding loss of the former approaches. The different algorithms are compared on the basis of convergence analysis and simulation results.