Integrating renewable energy sources into an unbalanced distribution network requires fast and accurate extraction of fundamental frequency positive- and negative-sequence components from the unbalanced three-phase grid voltage signals. For this purpose, various methods are already available in the literature. Out of them, delayed signal cancellation (DSC) is prevalent. Conventional DSC can separate the sequence components using a quarter-cycle delay. Fast DSC tools can achieve the same with less than a quarter-cycle delay. However, neither conventional nor fast DSC can handle DC offset without requiring additional delayed signals. This article addresses this issue by proposing a mod- ified DSC to estimate the sequence components with DC offset rejection and having arbitrarily fast convergence speed, i.e., low memory requirement. Two equidistant delayed samples of the measured grid voltages/currents are required to implement the proposed technique and can easily be applied in a phase-locked loop (PLL). Comparative experimen- tal results demonstrate the suitability of the proposed approach over other DSC methods.