A new algorithm for dynamic independent vector extraction is proposed. It is based on the mixing model where mixing parameters related to the source-of-interest (SOI) are time-variant while the separating parameters are time-invariant. A contrast function based on the quasi-likelihood approach is optimized using the Newton-Raphson approach. The update is computed without imposing the orthogonal constraint, and the orthogonality is enforced afterward. This yields an algorithm that is significantly faster than gradient-based algorithms while different from fixed-point methods, which are even faster. We show advantageous properties of the proposed algorithm compared to the fixed-point methods in an on-line processing regime where stable convergence to the SOI is the important issue. The effectiveness of the method is demonstrated in a speech extraction experiment with a dense microphone array.