# Base change to make singular points on singular fibers split

Let $$C$$ be a semi-stable curve over $$Spec(O_K)$$ where $$K$$ is an algebraic number field.

Assume that $$X_s$$ is singular for $$s\in Spec(O_K)$$. How do we know that there exists a finite separable extension $$k'$$ of $$k(s)$$ such that the singular points of $$X_s\times_{Spec(k(s))}Spec(k')$$ are split?

On Liu's book "Algebraic Geometry and Arithmetic Curves", p514, Cor 3.22 (a)'s proof, it said that 'by the virtue of Prop 3.7(c)' which makes me confused.