In the present paper, by pointing out some errors in reference [17], we know that the well-known integer distance point problem of Steinhaus is still open. Using the result of Galois extension, we discuss the Steinhaus problem for some quadrilaterals. In fact, we show that for the case of quadrilaterals which the sum of a pair of corner is \frac{2k\pi}{n}, where n\geq 7, k
