In this paper, a hybrid three-step approach is introduced to bring the data to approximate normality. This approach uses two different transformations jointly with flipping and, in some cases, with Winsorization. The first step is to achieve approximate symmetry by transforming the data using the generalized modulus family of transformations. If the quantile to be estimated is in the longer tail, the resulting transformed sample is then Winsorized. The second step is to achieve exact sample symmetry by flipping the lower (upper) half of the transformed sample when estimating quantiles smaller (larger) than the median. The third step is to approximately Gaussianize the resulting sample using the sinh-arcsinh transformation. Estimating the quantile of the new data and then double back transforming, the new proposed nonparametric quantile estimator can be obtained. Through a simulation study, the new proposed quantile estimator is evaluated and compared with some competitor existing estimators. Simulation results show stable empirical performance and unrestricted outperformance of the proposed estimator compared to all other competitor estimators under investigation.