© 2020 by the authors. Licensee MDPI, Basel, Switzerland. Quaternion orthogonal designs (QODs) have been used to design STBCs that provide improved performance in terms of various design parameters. In this paper, we show that all QODs obtained from generic iterative construction techniques based on the Adams-Lax-Phillips approach have linear and decoupled decoders which significantly reduce the computational complexity at the receiver. Our result is based on the quaternionic description of communication channels among dual-polarized antennas. Another contribution of this work is the linear and decoupled decoder for quasi-orthogonal codes for non-square as well as square designs. The proposed solution promises diversity gains with the quaternionic channel model and the decoding solution is independent of the number of receive dual-polarized antennas. A brief comparison is presented at the end to demonstrate the effectiveness of quaternion designs in two dual-polarized antennas over available STBCs for four single-polarized antennas. Linear and decoupled decoding of two quasi-orthogonal designs is shown, which has failed to exit previously. In addition, a QOD for 2 × 1 dual-polarized antenna configuration using quaternionic channel model shows a 3 dB gain at 10−5 in comparison to the same code evaluated for 2 × 2 complex representation of the quaternionic channel. This gain is further enhanced when the received diversity for these the cases is matched i.e., 2 × 2. The code using the quaternionic channel model shows a further 13 dB improvement at 10−5 BER.