Although the Feedback-based Two-stage Switch Architecture (FTSA) shows excellent performances in simulation, it can not be realized under present technology condition because of the time restrictions on the scheduling algorithms. To relax the time constraint of the FTSA, this paper proposed an improved two-stage switch architecture called FTSA-2-SS (FTSA using the 2-Staggered Symmetry connection pattern), which enables the cell transmission to take place in parallel with the scheduling process with the adoption of 2-staggered symmetry connection pattern and thus extends the time space of the scheduling algorithm to the whole time slot. In addition, FTSA-2-SS uses the double-cell-buffer mode and Re-sequencing Buffer (RB) to solve the consequent problem such as cell conflict and disordering. Theoretical analysis shows that FTSA-2-SS has the same stability as FTSA and the simulation results show that FTSA-2-SS has a better delay performance compared with the other non-feedback two-stage switch architecture.