Let G be a locally compact Hausdorff topological group and H be a compact subgroup of G. Then, the homogeneous space G/H possesses a specific Radon measure, which is called a relatively invariant measure. We show that the concepts of convolution and involution can be extended to the integrable functions defined on this homogeneous space. We study the properties of convolution and prove that the space of integrable functions is an involutive Banach algebra with an approximate identity. We also find a necessary and sufficient condition on a closed subspace of this Banach algebra to make it a left ideal.