Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) said that the Prophet (peace and blessings be upon him) would not leave these two corners, the Yamani Corner and the Black Stone, in any circuit; he would touch them both, and he would not touch the two that are next to the Hijr (the Hatim).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9259