This study experimentally investigated an active flow control method with combined jets at the front and the rear stagnation points of a square cylinder to suppress the unsteady wake flow. The Reynolds number (Re) was $1.67\times {10}^4$ , based on the incoming speed of airflow and the diameter of test model. The square cylinder model was manufactured with two narrow slots symmetrically positioned at the centerline of the front and rear surfaces. The strength of the jets is characterized with a dimensionless momentum coefficient $C_{\mu }$ . We obtained the dynamic wake flow regimes by employing the particle image velocimetry technique. Then, with the method of proper orthogonal decomposition and linear stability analysis, the time-averaged flow characteristics, e.g., turbulence kinetic energy (TKE) and the Reynolds shear stress (RSS) distributions, and the dynamic wake flow behind the square cylinder were analyzed in detail. Results of flow visualization suggested that at low momentum coefficient $C_{\mu }$ the wake flow regime showed no notable modifications to the wake. As $C_{\mu }$ increased to 0.0948, the periodic shear layers from the square cylinder were found to be pushed to the farther wake. Meanwhile, the time-averaged wake flow region was found to be greatly modified in the streamwise direction with a notable decrease in TKE and RSS distributions. The experimental results indicated that unsteadiness of vortex shedding in the wake flow experienced notable suppression. For higher $C_{\mu }$ up to 0.2133 and 0.3793, unsteady vortex shedding from the square cylinder and the dynamic wake flow were further suppressed in the near wake. A linear stability analysis was also employed to reveal the underlying nature of wake modification by the combined jets.