Let \(w=f(z)\) be a non-constant entire function of a complex variable z and let D be a non-empty simply connected domain where \(w=f(z)\) is univalent. Let \(A_ 1A_ 2A_ 3A_ 4\) be an arbitrary rectangle contained entirely in D whose sides are parallel to the real and imaginary axes on the z-plane. Here the four vertices \(A_ 1,A_ 2,A_ 3,A_ 4\) are listed consecutively. We put \(A'_ k=f(A_ k)\) \((k=1,2,3,4)\) on the w-plane. We consider the following two conditions: (C.1) \(\overline{A'_ 1A'_ 3}=\overline{A'_ 2A'_ 4}\). (C.2) Let EF be an arbitrary line segment contained entirely in D with midpoint M and let \(E'=f(E)\), \(F'=f(F)\), \(M'=f(M)\) on the w-plane. (i) If EF is parallel to the real axis on the z-plane, then the tangent line to the arc f(EF) at M' is parallel to the chord E'F' joining its extremities on the w- plane. (ii) If EF is parallel to the imaginary axis on the z-plane, then the tangent line to the arc f(EF) at M' is parallel to the chord E'F' joining its extremities on the w-plane. The purpose of the present note is to prove the following theorem: Theorem. Let \(w=f(z)\) be a non-constant entire function of z. (a) Condition (C.1) and condition (C.2) (i) are equivalent. (b) Condition (C.1) and condition (C.2) (ii) are equivalent. Furthermore, the author determines all entire functions f(z) satisfying (C.2) (i) or (ii) by using his previous result on (C.1) and the above theorem.