The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. In this paper, we study the relative Baum-Connes assembly map for any pair of groups and apply it to solve the relative Novikov conjecture when the groups satisfy certain geometric conditions. Contents 1. Introduction 2. The relative Novikov conjecture 2.1. Roe algebras and localization algebras 2.2. Rips complex 2.3. Relative Roe algebras and relative localization algebras 3. Relative Baum-Connes conjecture 3.1. Relative reduced assembly map 3.2. Relative Baum-Connes conjecture for hyperbolic groups 4. A relative Bott Periodicity 4.1. C * -algebras associated with Hilbert spaces 4.2. C * -algebra with group actions 5. The proofs of the main results 5.1. The maximal strong relative Novikov conjecture 5.2. The reduced strong relative Novikov conjecture 6. Applications to the relative Novikov conjecture References