If \((K,+,\cdot,\leq)\) is an ordered commutative field, \(L=K(i)\) with \(i^ 2=-1\) a quadratic extension and \(z=x+iy\to\overline{z}:=x-iy\) the involutory \(K\)-automorphism, then one can define in the set \(\mathfrak M\) of all \(2\times 2\)-matrices with coefficients in \(L\) the subset \({\mathfrak H}=\{X\in {\mathfrak M}\mid X^ T=\overline{X}\}\) of Hermitian matrices and furthermore the future cone ``\({\mathfrak H}^{++} :=\{X\in {\mathfrak H}\mid\text{Tr }X > 0,\;\text{det }X > 0\}\)''. For each \(A\in {\mathfrak H}^{++}\) the equation \(X^ 2=A\) has a solution \(X\in {\mathfrak H}^{++}\) iff \(K\) is Euclidean. \textit{H. Karzel} and \textit{H. Wefelscheid} [Result Math. 23, No. 3-4, 338-354 (1993; Zbl 0788.20034)] showed that in this case \(({\mathfrak H}^{++},\oplus)\) is a \(K\)-loop with respect to the operation \(A\oplus B :=\sqrt{A} B\sqrt{A}\) (where \(\sqrt{A}\in {\mathfrak H}^{++}\) is defined by \(\sqrt{A}\cdot\sqrt{A}=A\)). The author shows: Also in the case of arbitrary ordered fields \((K,+,\cdot,\leq)\) one can obtain examples of \(K\)-loops if one considers the subset \({\mathfrak H}^{(2),+} :=\{X\in {\mathfrak H}^{++}\mid\text{det }X\in K^{(2)}\}\) (where \(K^{(2)} :=\{\lambda^ 2\mid\lambda\in K\setminus\{0\}\}\)) of \({\mathfrak H}^{++}\). If \(\overline{K}\) is a Euclidean hull of \((K,+,\cdot,\leq)\), \(\overline{L} :=\overline{K}(i)\) with \(i^ 2=-1\) and \(\overline{{\mathfrak H}}\) the Hermitian \(2\times 2\)- matrices over \((\overline{L},\overline{K})\) then \(({\mathfrak H}^{(2),+},\oplus)\) is a subloop of \((\overline{\mathfrak H}^{++},\oplus)\).