diff --git a/ext/TensorKitChainRulesCoreExt.jl b/ext/TensorKitChainRulesCoreExt.jl
index 514d4749..6ff4b791 100644
--- a/ext/TensorKitChainRulesCoreExt.jl
+++ b/ext/TensorKitChainRulesCoreExt.jl
@@ -172,7 +172,9 @@ end
 function ChainRulesCore.rrule(::typeof(norm), a::AbstractTensorMap, p::Real=2)
     p == 2 || error("currently only implemented for p = 2")
     n = norm(a, p)
-    norm_pullback(Δn) = NoTangent(), a * (Δn' + Δn) / (n * 2), NoTangent()
+    function norm_pullback(Δn)
+        return NoTangent(), a * (Δn' + Δn) / 2 / hypot(n, eps(one(n))), NoTangent()
+    end
     return n, norm_pullback
 end