The faint coronal structure existing prior to high-latitude X-ray arcade formation oberved by the Yohkoh Soft X-ray Telescope has turned out to be "overlapped dual arcades" whose inside legs cross with one another, rather than being a simple bipolar arcade whose top part is sagging due to loading of the dark filament material, as considered in previous models of dark filament suspension. The photospheric magnetic field under the crossed legs is found to be a belt of mixed polarity, extending tens of thousand kilometers, rather than a clean border of the two extended unipolar regions. The magnetic field distribution, as well as the coronal structure above it, are very different from the previously assumed situation for dark filaments based on the assumption of a bipolar photospheric magnetic field distribution. The coronal structure found in the region, the "overlapped dual arcades" structure, is most likely to be the "separatrix surfaces" in the quadruple photospheric magnetic source model for the magnetic configuration surrounding a dark-filament, as proposed by one of the present authors in his previous work (Uchida 1980, AAA 28.073.129).