We discuss the possibility of the spontaneous symmetry breaking characterized by order parameters with higher dimensionful composite fields. By analyzing general Ginzburg-Landau potential for a complex scalar field \phi=\phi_1 + i \phi_2 with O(2) symmetry, we demonstrate that a phase characterized by < \phi_1^2 - \phi_2^2 > \neq 0 with < \phi_1 >=< \phi_2 >=0 is realized in a certain parameter region. To clarify the driving force to favor this phase, we study the O(2) \phi^6 theory in three dimensions.