diff --git a/flag.go b/flag.go
index 362a20a..06fb7a8 100644
--- a/flag.go
+++ b/flag.go
@@ -421,7 +421,10 @@
 }
 
 func (f *FlagSet) AddFlag(flag *Flag) {
-	_, alreadythere := f.formal[f.normalizeFlagName(flag.Name)]
+	// Call normalizeFlagName function only once
+	var normalizedFlagName NormalizedName = f.normalizeFlagName(flag.Name)
+
+	_, alreadythere := f.formal[normalizedFlagName]
 	if alreadythere {
 		msg := fmt.Sprintf("%s flag redefined: %s", f.name, flag.Name)
 		fmt.Fprintln(f.out(), msg)
@@ -430,7 +433,7 @@
 	if f.formal == nil {
 		f.formal = make(map[NormalizedName]*Flag)
 	}
-	f.formal[f.normalizeFlagName(flag.Name)] = flag
+	f.formal[normalizedFlagName] = flag
 
 	if len(flag.Shorthand) == 0 {
 		return
diff --git a/flag_test.go b/flag_test.go
index b5956fa..efd6666 100644
--- a/flag_test.go
+++ b/flag_test.go
@@ -17,14 +17,15 @@
 )
 
 var (
-	test_bool     = Bool("test_bool", false, "bool value")
-	test_int      = Int("test_int", 0, "int value")
-	test_int64    = Int64("test_int64", 0, "int64 value")
-	test_uint     = Uint("test_uint", 0, "uint value")
-	test_uint64   = Uint64("test_uint64", 0, "uint64 value")
-	test_string   = String("test_string", "0", "string value")
-	test_float64  = Float64("test_float64", 0, "float64 value")
-	test_duration = Duration("test_duration", 0, "time.Duration value")
+	test_bool                    = Bool("test_bool", false, "bool value")
+	test_int                     = Int("test_int", 0, "int value")
+	test_int64                   = Int64("test_int64", 0, "int64 value")
+	test_uint                    = Uint("test_uint", 0, "uint value")
+	test_uint64                  = Uint64("test_uint64", 0, "uint64 value")
+	test_string                  = String("test_string", "0", "string value")
+	test_float64                 = Float64("test_float64", 0, "float64 value")
+	test_duration                = Duration("test_duration", 0, "time.Duration value")
+	normalizeFlagNameInvocations = 0
 )
 
 func boolString(s string) string {
@@ -254,6 +255,8 @@
 func wordSepNormalizeFunc(f *FlagSet, name string) NormalizedName {
 	seps := []string{"-", "_"}
 	name = replaceSeparators(name, seps, ".")
+	normalizeFlagNameInvocations++
+
 	return NormalizedName(name)
 }
 
@@ -574,3 +577,16 @@
 		t.Errorf("usageMsg not printed when using a deprecated flag!")
 	}
 }
+
+// Name normalization function should be called only once on flag addition
+func TestMultipleNormalizeFlagNameInvocations(t *testing.T) {
+	normalizeFlagNameInvocations = 0
+
+	f := NewFlagSet("normalized", ContinueOnError)
+	f.SetNormalizeFunc(wordSepNormalizeFunc)
+	f.Bool("with_under_flag", false, "bool value")
+
+	if normalizeFlagNameInvocations != 1 {
+		t.Fatal("Expected normalizeFlagNameInvocations to be 1; got ", normalizeFlagNameInvocations)
+	}
+}