Abstract: The stepwise high precision winding method includes winding the yarn on the bobbin with a reciprocating yarn changing guide in a series of steps so that an outer circumferential speed of the yarn-bobbin package is constant; reducing the yarn guide reciprocation frequency in each step from a starting frequency value to a final frequency value while keeping a winding number constant during each step so that the final frequency value is proportional to a bobbin rotation frequency in each step, and then increasing the yarn guide reciprocation frequency discontinuously to another starting frequency value and beginning a following step with the yarn guide reciprocation frequency equal to the other starting frequency value; setting the starting frequency value in each step to not more than a fixed maximum frequency; setting the final frequency value in each step to not less than a certain fixed minimum frequency; and setting the winding number in the Sth step equal to either i.sub.S -i.sub.S x/(M.sub.S +x) or i.sub.