diff --git a/stdlib/LinearAlgebra/src/generic.jl b/stdlib/LinearAlgebra/src/generic.jl
index ca747db604fc8..31a02a40e8a24 100644
--- a/stdlib/LinearAlgebra/src/generic.jl
+++ b/stdlib/LinearAlgebra/src/generic.jl
@@ -466,7 +466,21 @@ julia> norm(-2, Inf)
 2
 ```
 """
-@inline norm(x::Number, p::Real=2) = p == 0 ? (x==0 ? zero(abs(x)) : oneunit(abs(x))) : abs(x)
+@inline function norm(x::Number, p::Real=2)
+    afx = abs(float(x))
+    if p == 0
+        if x == 0
+            return zero(afx)
+        elseif !isnan(x)
+            return oneunit(afx)
+        else
+            return afx
+        end
+    else
+        return afx
+    end
+end
+
 norm(::Missing, p::Real=2) = missing
 
 # special cases of opnorm
diff --git a/stdlib/LinearAlgebra/test/generic.jl b/stdlib/LinearAlgebra/test/generic.jl
index 13d18e1d29b23..e4b7cfaa49057 100644
--- a/stdlib/LinearAlgebra/test/generic.jl
+++ b/stdlib/LinearAlgebra/test/generic.jl
@@ -186,11 +186,15 @@ end
         @test issymmetric(a)
         @test ishermitian(one(elty))
         @test det(a) == a
+        @test norm(a) == abs(a)
+        @test norm(a, 0) == 1
     end
 
     @test !issymmetric(NaN16)
     @test !issymmetric(NaN32)
     @test !issymmetric(NaN)
+    @test norm(NaN)    === NaN
+    @test norm(NaN, 0) === NaN
 end
 
 @test rank(fill(0, 0, 0)) == 0