We study the phenomenological implications of the recent neutrino data for class B of two texture zeros and two vanishing cofactors for Majorana neutrinos in the flavor basis. We find that the classes $$B_{1}$$ B 1 ( $$B_2$$ B 2 ) of two texture zeros and the classes $$B_5$$ B 5 ( $$B_6$$ B 6 ) of two vanishing cofactors have similar predictions for neutrino oscillation parameters for the same mass hierarchy. Similar predictions for the classes $$B_3$$ B 3 ( $$B_4$$ B 4 ) of two texture zeros and classes $$B_3$$ B 3 ( $$B_4$$ B 4 ) of two vanishing cofactors are expected. However, a preference for a shift in the quadrant of the Dirac-type CP-violating phase ( $$\delta $$ δ ) in contrast to the earlier analysis has been predicted for a relatively large value of the reactor neutrino mixing angle ( $$\theta _{13}$$ θ 13 ) for class B of two texture zeros and two vanishing cofactors for an inverted mass spectrum. No such shift in the quadrant of $$\delta $$ δ has been found for the normal mass spectrum.