PURPOSE: To eliminate great differences in temperatures on upper side separating walls forming each region by dividing a cavity of a continuous furnace into a plurality of sections and prevent damage of the upper side separating walls from being caused by such temperature differences.

CONSTITUTION: A plurality of longitudinal grooves 11c, 11d extending vertically so as to be opposed to an upper edge of each underlaying separating wall 12 are provided on a top wall 11b above a transfer passage in a furnace main body 11 and on both right and left side walls 11a positioned on either side of the transfer passage, and a heat-resistant receiving member 17 extending in a lateral direction across a cavity is provided on the bottom of each longitudinal groove 11d, whereby the lower end of each upper side separating wall 13 is received by the receiving member 17 in such a state that each upper side separating wall 13 is inserted into each longitudinal groove 11c, 11d. In addition, the upper end of each upper side separating wall 13 is supported on the top wall 11b of the furnace main body 11 in a state of shutting off the external side, and great differences in temperatures on the upper side separating walls 13 are prevented from being caused.