Let L/F be a finite separable extension of Henselian valued fields with same residue fields $overline{L} = overline{F}$. Let D be an inertially split division algebra over L, and let $^cD$ be the underlying division algebra of the corestriction $cor_{L/F} (D)$ of D. We show that the index $ind(^cD) of ^cD$ divides $[Z(overline{D}) : Z(overline {^cD})] cdot ind(D), where Z(overline{D})$ is the center of the residue division ring $overline{D}$.