FormStyle: Border Flat

TForm1 = class(TForm)
  procedure CreateParams(var Params: TCreateParams); override;
  procedure WMActivate(Var msg:tMessage); message WM_ACTIVATE;

procedure TForm1.CreateParams(var Params: TCreateParams);
begin
  inherited;
  Params.Style := WS_POPUP or WS_THICKFRAME;
end;

procedure TForm1.WMActivate(var msg: tMessage);
begin
  if Msg.WParam = WA_INACTIVE then
    Hide;
end;