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In this paper, an enhanced version of the opposition-based differential evolution (ODE) is proposed. ODE utilizes opposite numbers in the population initialization and generation jumping to accelerate differential evolution (DE). Instead of opposite numbers, in this work, quasi opposite points are used. So, we call the new extension quasi- oppositional DE (QODE). The proposed mathematical proof shows that in a black-box optimization problem quasi- opposite points have a higher chance to be closer to the solution than opposite points. A test suite with 15 benchmark functions has been employed to compare performance of DE, ODE, and QODE experimentally. Results confirm that QODE performs better than ODE and DE in overall. Details for the proposed approach and the conducted experiments are provided.