Abstract In this paper we deal with those Banach spaces Z which satisfy the Mazur–Ulam property, namely that every surjective isometry Δ from the unit sphere of Z to the unit sphere of any Banach space Y admits a unique extension to a surjective real-linear isometry from Z to Y. We prove that for every countable set Γ with | Γ | ≥ 2 , the Banach space ⨁ γ ∈ Γ c 0 X γ satisfies the Mazur–Ulam property, whenever the Banach space X γ is strictly convex with dim ( ( X γ ) R ) ≥ 2 for every γ. As a consequence, every weakly countably determined Banach space can be equivalently renormed so that it satisfies the Mazur–Ulam property.