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The iron-selenides are important because of their superconducting properties.Here, an unexpected phenomenon is predicted to occur in an iron-selenidecompound with a quasi-one-dimensional ladder geometry: BaFe$_2$Se$_3$ should bea magnetic ferrielectric system, driven by its magnetic block order viaexchange striction. A robust performance (high $T_{\rm C}$ and largepolarization) is expected. Different from most multiferroics, BaFe$_2$Se$_3$ isferrielectric, with a polarization that mostly cancels between ladders.However, its strong magnetostriction still produces a net polarization that islarge ($\sim$$0.1$ $\mu$C/cm$^2$) as compared with most magnetic multiferroics.Its fully ferroelectric state, with energy only slightly higher than theferrielectric, has a giant improper polarization $\sim$$2-3$ $\mu$C/cm$^2$.

BaFe$_2$Se$_3$: a high $T_{\rm C}$ magnetic multiferroic with large ferrielectric polarization