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We introduce an extension to the conventional variation after projection (VAP) method, in which wave functions of different spin states projected from a shared intrinsic wave function are first varied simultaneously. Then a second variation is carried out for each individual state starting from the obtained intrinsic wave function. This novel algorithm enables the efficient extraction of a rotational band from chaotic non-rotational states by adopting only one Slater determinant, which can not be reached by the conventional VAP method. Some examples including the heavy deformed nuclei in the jj56 model space have been calculated. The calculated results show that this new method could be a useful tool to systematically study the collective rotational states in heavy deformed nuclei. Furthermore, the present method holds potential for probing significant correlations, such as octupole correlations, within nuclear structures.