The inertial migration of neutrally buoyant spherical particles in square channel flows was investigated experimentally in the range of Reynolds numbers ($\mathit{Re}$) from 100 to 1200. The observation of particle positions at several cross-sections downstream from the channel entrance revealed unique patterns of particle distribution which reflects the presence of eight equilibrium positions in the cross-section, located at the centres of the channel faces and at the corners, except for low $\mathit{Re}$. At $\mathit{Re}$ smaller than approximately 250, equilibrium positions at the corners are absent. The corner equilibrium positions were found to arise initially in the band formed along the channel face, followed by a progressive shift almost parallel to the side wall up to the diagonal line with increasing $\mathit{Re}$. Further increase in $\mathit{Re}$ moves the corner equilibrium positions slightly toward the channel corner, whereas the equilibrium positions at the channel face centres are shifted toward the channel centre. As the observation sites become downstream, the particles were found to be more focused near the equilibrium positions keeping their positions almost unchanged. These lateral migration behaviours and focusing properties of particles in square channels are different to that observed in microchannels at lower $\mathit{Re}$ and to what would be expected from extrapolating from the results for circular pipes at comparable $\mathit{Re}$.