It's not possible using .NET properties or methods as far as I'm aware. That icon is there so that you can click it to get the system menu for the child form. Even if you set the ControlBox property to False, which removes the system menu, Close button, etc. when the form is in a normal state, that icon is still visible and you can still click it to display the system menu. If it's possible to get rid of it it would require using the Windows API.

Also, shouting at those whom you want to help you is not productive. Even if the advice you get doesn't help you are no worse off than you were before. Noone here has any responsibility to be right, or help you at all for that matter.