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We generalize wave maps to biwave maps. We prove that the composition of a biwave map and a totally geodesic map is a biwave map. We give examples of biwave nonwave maps. We show that if 𝑓 is a biwave map into a Riemannian manifold under certain circumstance, then 𝑓 is a wave map. We verify that if 𝑓 is a stable biwave map into a Riemannian manifold with positive constant sectional curvature satisfying the conservation law, then 𝑓 is a wave map. We finally obtain a theorem involving an unstable biwave map.