To continuously and stably produce an undrawn polyester yarn (a partially oriented yarn) having a favorable color tone with slight quality unevenness and a degree of molecular orientation of 0.03-0.06 as a birefringence index over a long period.

A deposit obtained by heating a specific titanium compound and a specified phosphorus compound in a glycol so as to provide the ratio (P/Ti)of the number of mol of the phosphorus elements to the number of mol of the titanium elements within the range of 1-4 is used as a catalyst. A synthesized polyethylene terephthalate polyester is melted, spun and taken off at 2,500-4,000 m/min speed while being cooled/solidified to afford 0.03-0.06 birefringence index.