bundling agent to fix the direction to lateral direction of fibers the bundling agents used for such a purpose include ethyl alcohol a mixture of ethyl alcohol with water and a mixture of ethyl alcohol with a silicone oil aqueous emulsion it is preferred that the filament number of the fiber bundle be not more than 10 000 the pitch fibers tend to slightly shrink in the infusibilization step and therefore the bundled fiber is disturbed when the thus disturbed bundle is carbonized the direction of torsion is disturbed and a good coil shaped product cannot be obtained we have now found that a coil shaped fiber bundle having the same coil direction and having excellent stretchability can be obtained by infusibilizing the bundle of the fibers obtained under conditions as described above under tension and carbonizing it while the infusibilization step can be suitably adjusted depending upon types of the spinning pitches used and combinations thereof the infusibilization is preferably carried out under a tension of at least 0 0001 gram per each filament and more preferably at least about 0 0004 grams per each filament while the carbonization step is desirably carried out substantially under a non tension the tension force of no more than 0 05 grams per each filament may be present if the tension of more than 0 05 grams per each filament is applied during carbonization the difference in the percent linear shrinkage of composited pitches will be.