diff --git a/src/manifolds/ProductManifold.jl b/src/manifolds/ProductManifold.jl
index 99d7f3be3c..ef90452df2 100644
--- a/src/manifolds/ProductManifold.jl
+++ b/src/manifolds/ProductManifold.jl
@@ -659,7 +659,7 @@ function injectivity_radius(M::ProductManifold, p, m::AbstractRetractionMethod)
         )...,
     )
 end
-function _injectivity_radius(M::ProductManifold, p, m::ProductRetraction)
+function injectivity_radius(M::ProductManifold, p, m::ProductRetraction)
     return min(
         map(
             (lM, lp, lm) -> injectivity_radius(lM, lp, lm),
@@ -673,7 +673,7 @@ injectivity_radius(M::ProductManifold) = min(map(injectivity_radius, M.manifolds
 function injectivity_radius(M::ProductManifold, m::AbstractRetractionMethod)
     return min(map(manif -> injectivity_radius(manif, m), M.manifolds)...)
 end
-function _injectivity_radius(M::ProductManifold, m::ProductRetraction)
+function injectivity_radius(M::ProductManifold, m::ProductRetraction)
     return min(map((lM, lm) -> injectivity_radius(lM, lm), M.manifolds, m.retractions)...)
 end
 
@@ -728,18 +728,6 @@ for TP in [ProductRepr, ArrayPartition]
     )
 end
 
-function _inverse_retract!(M::ProductManifold, X, p, q, method::InverseProductRetraction)
-    map(
-        inverse_retract!,
-        M.manifolds,
-        submanifold_components(M, X),
-        submanifold_components(M, p),
-        submanifold_components(M, q),
-        method.inverse_retractions,
-    )
-    return X
-end
-
 function Base.isapprox(M::ProductManifold, p, q; kwargs...)
     return all(
         t -> isapprox(t...; kwargs...),
diff --git a/test/manifolds/product_manifold.jl b/test/manifolds/product_manifold.jl
index c74a05974c..b01be0a5e3 100644
--- a/test/manifolds/product_manifold.jl
+++ b/test/manifolds/product_manifold.jl
@@ -15,6 +15,11 @@ using RecursiveArrayTools: ArrayPartition
     @test Mse[1] == M1
     @test Mse[2] == M2
     @test injectivity_radius(Mse) ≈ π
+    @test injectivity_radius(
+        Mse,
+        ProductRetraction(ExponentialRetraction(), ExponentialRetraction()),
+    ) ≈ π
+    @test injectivity_radius(Mse, ExponentialRetraction()) ≈ π
     @test injectivity_radius(
         Mse,
         ProductRepr([0.0, 1.0, 0.0], [0.0, 0.0]),