PURPOSE: To stably obtain a billet having no drawing mark by interposing a connecting refractory between a tundish and mold so as to serve as the bottom wall face close to the pouring port provided at the bottom of a tundish as well.

CONSTITUTION: A continuous casting is performed in the type that a tundish 6 and hold 2 are linked with a connecting refractory 1 and an ingot is continuously or intermittently drawn. In this case, the heat conduction from the molten steel 7 inside the tundish 6 is utilized for heating of the connecting refractory 1 by serving it also as the role for the bottom part refractory of the tundish 6. The solidifying shell 8 formed from the connecting refractory 1 side is thus made to be eliminated. The billet having no drawing marks is stably obtd.