Distance measure is a basic concept in Pythagorean fuzzy decision making, it plays an important role in the ordered aggregation operation, ordered weighted distance evaluation and construction of similarity through a weight vector. However, in the early article Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets published in the famous journal International Journal of Intelligent Systems, which is the first paper to introduce the Hamming distance measure, and many authors cited the concept of distance measure later, it is found that the method of proving the axiomatization conditions of distance is inappropriate. We demonstrate counterexamples to show that there are two serious errors in proving the boundness and three-point inequality in the axiomatization conditions. Alternatively, we consider the absolute value term of hesitation degree and other absolute value terms as a whole, and an improved strict proof of the Hamming distance measure is given by analysis and discussion. In addition, it is proved that the extended form of Hamming distance (Euclid distance measure) satisfies the axiomatic conditions.