In this paper, the rheological characteristics of aqueous PEO (Polyethylene oxide) solution with very high molecular weight 4x106 g/mol is investigated. Shear flow measurements were carried out in steady and transient modes. The unique behavior of PEO is found to be heavily dependent on the input shear rate and the mechanism of data generation. Generally, PEO is found to be shear-thinning throughout the experiments, but at the start of the experiments at low shear rates, minimum input shear value also affects the shear-thinning behavior. In this study, we investigate the critical method of applying input shear to the samples in the lower shear rate regime. Surprisingly, different input methods yield different results. Viscosity curves obtained through shear flow experiments are found to be significantly dependent on the input method of shear rate. Experimental measurements were validated by Cross and Carreau-Yasuda models.