The conductance quantization and shot noise below the first conductance plateau G0=2e2/h are measured in a quantum point contact fabricated in a GaAs/AlGaAs tunnel-coupled double quantum well. From the conductance measurement, we observe a clear quantized conductance plateau at 0.5G0 and a small minimum in the transconductance at 0.7G0. Spectroscopic transconductance measurement reveals three maxima inside the first diamond, thus suggesting three minima in the dispersion relation for electric subbands. Shot noise measurement shows that the Fano factor behavior is consistent with this observation. We propose a model that relates these features to a wave-number directional split subband due to a strong Rashba spin-orbit interaction that is induced by the center barrier potential gradient of the double-layer sample.