a spinneret having circular spinning holes of 1 0 mm in diameter the total number of spinning holes 240 at a rate of 100 g min at a spinning temperature of 240 u00b0 c extruded through the spinning holes and drawned at a rate of 428 m min to obtain composite micro fibers generating fibers of sheath and core type the cross section of the undrawned fibers was observed by a microscope as a result the sheath component having an island in sea structure was present surrounding the core component the number of the islands being several hundreds the resulting micro fibers generating conjugate fibers were drawned to four times the original length to obtain drawned micro fibers generating conjugate fibers further the fibers were cut into those of 3 mm followed by subjecting them to wet paper processing to obtain a non woven fabric of micro fibers of polypropylene of 0 02 to 0 1 denier and normal fiber of 2 2 denier and having a basis weight of 100 g m 2 the resulting non woven fabric had a break strength of about 0 8 kg per test piece of 5 cm wide and 10 cm in length the micro fibers generating conjugate fibers of the present invention comprise a part having an island in sea structure which generates micro fibers of 0 1 denier or less and the other part which generates fibers of 0 5 denier or more hence the fibers have a high.