Assuming that this question is about the government of the United States, the statement is false. The head of the Department of State (also called the State Department) does have the title of secretary. The head of this department is called the Secretary of State. The current Secretary of State is John Kerry.
In the government of the United States, the heads of almost all of the main departments of the government have the title of secretary. We have such department heads as the Secretary of Defense and the Secretary of Commerce. The only major department whose head is not called "secretary" is the Department of Justice. That department's head is called the Attorney General.
In most other countries, heads of departments do not have the title of secretary. Instead, they are called ministers. The German equivalent of the Secretary of State, for example, is called the Minister of Foreign Affairs.