diff --git a/jerry-core/ecma/operations/ecma-function-object.c b/jerry-core/ecma/operations/ecma-function-object.c
index 8cbf3ce2f..befad242c 100644
--- a/jerry-core/ecma/operations/ecma-function-object.c
+++ b/jerry-core/ecma/operations/ecma-function-object.c
@@ -2248,7 +2248,8 @@ ecma_op_function_list_lazy_property_names (ecma_object_t *object_p, /**< functio
 #endif /* JERRY_ESNEXT */
 
 #if JERRY_ESNEXT
-  if (!CBC_FUNCTION_HAS_PROTOTYPE (bytecode_data_p->status_flags))
+  if (!CBC_FUNCTION_HAS_PROTOTYPE (bytecode_data_p->status_flags)
+      || (CBC_FUNCTION_GET_TYPE (bytecode_data_p->status_flags) == CBC_FUNCTION_CONSTRUCTOR))
   {
     return;
   }
diff --git a/jerry-core/parser/js/js-parser-expr.c b/jerry-core/parser/js/js-parser-expr.c
index bb22e43fa..c656a29d7 100644
--- a/jerry-core/parser/js/js-parser-expr.c
+++ b/jerry-core/parser/js/js-parser-expr.c
@@ -520,7 +520,8 @@ parser_is_constructor_literal (parser_context_t *context_p) /**< context */
  */
 static bool
 parser_parse_class_body (parser_context_t *context_p, /**< context */
-                         parser_class_literal_opts_t opts) /**< class literal parsing options */
+                         parser_class_literal_opts_t opts, /**< class literal parsing options */
+                         uint16_t class_name_index) /**< class literal index */
 {
   JERRY_ASSERT (context_p->token.type == LEXER_LEFT_BRACE);
 
@@ -541,6 +542,11 @@ parser_parse_class_body (parser_context_t *context_p, /**< context */
     parser_emit_cbc_ext (context_p, CBC_EXT_PUSH_IMPLICIT_CONSTRUCTOR);
   }
 
+  if (class_name_index != PARSER_INVALID_LITERAL_INDEX)
+  {
+    parser_emit_cbc_ext_literal (context_p, CBC_EXT_SET_CLASS_NAME, class_name_index);
+  }
+
   parser_emit_cbc_ext (context_p, CBC_EXT_INIT_CLASS);
 
   bool is_static = false;
@@ -1014,12 +1020,11 @@ parser_parse_class (parser_context_t *context_p, /**< context */
   }
 
   /* ClassDeclaration is parsed. Continue with class body. */
-  bool has_static_field = parser_parse_class_body (context_p, opts);
+  bool has_static_field = parser_parse_class_body (context_p, opts, class_name_index);
 
   if (class_name_index != PARSER_INVALID_LITERAL_INDEX)
   {
     parser_emit_cbc_ext_literal (context_p, CBC_EXT_FINALIZE_NAMED_CLASS, class_name_index);
-    parser_emit_cbc_ext_literal (context_p, CBC_EXT_SET_CLASS_NAME, class_name_index);
     PARSER_MINUS_EQUAL_U16 (context_p->scope_stack_top, 1);
   }
   else
diff --git a/tests/jerry/es.next/class-fields3.js b/tests/jerry/es.next/class-fields3.js
index fac1fd697..9de4be0bb 100644
--- a/tests/jerry/es.next/class-fields3.js
+++ b/tests/jerry/es.next/class-fields3.js
@@ -78,6 +78,6 @@ let C3 = class C4 {
   static yy = this
 }
 
-assert(Reflect.ownKeys(C3).toString() === "length,prototype,f,name,xx,yy")
+assert(Reflect.ownKeys(C3).toString() === "length,name,prototype,f,xx,yy")
 check_property(C3, "xx", C3)
 check_property(C3, "yy", C3)
diff --git a/tests/test262-es6-excludelist.xml b/tests/test262-es6-excludelist.xml
index 0b02934d0..2b203c4fb 100644
--- a/tests/test262-es6-excludelist.xml
+++ b/tests/test262-es6-excludelist.xml
@@ -335,4 +335,7 @@
   <test id="language/expressions/assignment/fn-name-lhs-member.js"><reason>Outdated test, anonymous functions should now have a name property</reason></test>
   <test id="language/expressions/function/name.js"><reason>Outdated test, anonymous functions should now have a name property</reason></test>
   <test id="language/expressions/generators/name.js"><reason>Outdated test, anonymous functions should now have a name property</reason></test>
+  <test id="language/computed-property-names/class/static/method-number.js"><reason>ES12 15.7.14.15.d: The evaluation order has been changed</reason></test>
+  <test id="language/computed-property-names/class/static/method-string.js"><reason>ES12 15.7.14.15.d: The evaluation order has been changed</reason></test>
+  <test id="language/computed-property-names/class/static/method-symbol.js"><reason>ES12 15.7.14.15.d: The evaluation order has been changed</reason></test>
 </excludeList>
diff --git a/tests/test262-esnext-excludelist.xml b/tests/test262-esnext-excludelist.xml
index 00f28d23e..8cdf8def6 100644
--- a/tests/test262-esnext-excludelist.xml
+++ b/tests/test262-esnext-excludelist.xml
@@ -61,9 +61,6 @@
   <test id="language/block-scope/syntax/redeclaration/generator-name-redeclaration-attempt-with-async-function.js"><reason></reason></test>
   <test id="language/block-scope/syntax/redeclaration/generator-name-redeclaration-attempt-with-function.js"><reason></reason></test>
   <test id="language/block-scope/syntax/redeclaration/generator-name-redeclaration-attempt-with-generator.js"><reason></reason></test>
-  <test id="language/computed-property-names/class/static/method-number.js"><reason></reason></test>
-  <test id="language/computed-property-names/class/static/method-string.js"><reason></reason></test>
-  <test id="language/computed-property-names/class/static/method-symbol.js"><reason></reason></test>
   <test id="language/eval-code/direct/non-definable-function-with-function.js"><reason></reason></test>
   <test id="language/eval-code/direct/non-definable-function-with-variable.js"><reason></reason></test>
   <test id="language/eval-code/direct/non-definable-global-function.js"><reason></reason></test>