diff --git a/ext/TensorKitChainRulesCoreExt.jl b/ext/TensorKitChainRulesCoreExt.jl
index 47036534..6ff4b791 100644
--- a/ext/TensorKitChainRulesCoreExt.jl
+++ b/ext/TensorKitChainRulesCoreExt.jl
@@ -173,7 +173,7 @@ function ChainRulesCore.rrule(::typeof(norm), a::AbstractTensorMap, p::Real=2)
     p == 2 || error("currently only implemented for p = 2")
     n = norm(a, p)
     function norm_pullback(Δn)
-        return NoTangent(), a * (Δn' + Δn) / (n * 2 + eps(real(eltype(a)))), NoTangent()
+        return NoTangent(), a * (Δn' + Δn) / 2 / hypot(n, eps(one(n))), NoTangent()
     end
     return n, norm_pullback
 end