In the past decades, continuous Doppler radar sensor-based bio-signal detections have attracted many research interests.A typical example is the Doppler heartbeat detection. While significant progresses have been achieved, reliable, accurate demodulation of bio-signals in the presence of unavoidable DC offsets remains a technical challenge. Aiming to overcome this difficulty, we propose in this paper a novel demodulation algorithm that does not need to trace and eliminate dynamic DC offsets based on approximating segmented arcs in a quadrature constellation of sampling data to directional chords.Assisted by the principal component analysis, such chords and their directions can be deterministically determined.Simulations and experimental validations showed fully recovery of micron-level pendulum movements and strongly noised human heartbeats, verifying the effectiveness and accuracy of the proposed approach.