  We prove that a strengthened version of Minac-Tan's Massey Vanishing
Conjecture holds true for fields with a finite number of square classes whose
maximal pro-$2$ Galois group is of elementary type (as defined by I. Efrat). In
particular, this proves Minac-Tan's Massey Vanishing Conjecture for Pythagorean
fields with a finite number of square classes and their finite extensions.
