複数列の UNIQUE インデックスを作成するにはどうすればよいでしょうか?

mysql> Create UNIQUE INDEX id_fname_lname on employee(empid,first_name,last_name);
Query OK, 0 rows affected (0.41 sec)
Records: 0 Duplicates: 0 Warnings: 0

mysql> describe employee;
+------------+-------------+------+-----+---------+-------+
| Field | Type | Null | Key | Default | Extra |
+------------+-------------+------+-----+---------+-------+
| empid | int(11) | YES | MUL | NULL | |
| first_name | varchar(20) | YES | | NULL | |
| last_name | varchar(20) | YES | | NULL | |
+------------+-------------+------+-----+---------+-------+
3 rows in set (0.12 sec)

mysql> Show index from employee\G
*************************** 1. row ***************************
Table: employee
Non_unique: 0
Key_name: id_fname_lname
Seq_in_index: 1
Column_name: empid
Collation: A
Cardinality: 0
Sub_part: NULL
Packed: NULL
Null: YES
Index_type: BTREE
Comment:
Index_comment:
*************************** 2. row ***************************
Table: employee
Non_unique: 0
Key_name: id_fname_lname
Seq_in_index: 2
Column_name: first_name
Collation: A
Cardinality: 0
Sub_part: NULL
Packed: NULL
Null: YES
Index_type: BTREE
Comment:
Index_comment:
*************************** 3. row ***************************
Table: employee
Non_unique: 0
Key_name: id_fname_lname
Seq_in_index: 3
Column_name: last_name
Collation: A
Cardinality: 0
Sub_part: NULL
Packed: NULL
Null: YES
Index_type: BTREE
Comment:
Index_comment:
3 rows in set (0.00 sec)