Every finite-dimensional associative simple algebra \(D\) over a field is isomorphic to a matrix algebra over a division algebra \(B\). The index of \(D\) is the square root of the dimension of \(B\) over its center \(F\). The index reduction formula describes what happens with the index under field extensions of \(F\). The paper deals with the case when the field extension is the function field \(F(X)\), where \(X\) is a homogeneous variety of a reductive algebraic group over \(F\).