Let F be a field, , L/F a quartic field extension. Define by GL/F the group of elements r∈F⁎ such that D∪(r)=0 for any regular field extension K/F and any . We show that 05bc6d9ec6b78e162b45cf0ba" title="Click to view the MathML source">GL/F=F⁎2NL/FL⁎. As a consequence we prove that the Hasse norm theorem modulo squares holds for L/F.