octadecene and the like the u03b1 u03b2 unsaturated carboxylic acid may include acrylic acid methacrylic acid maleic anhydride fumaric acid itaconic acid and the like the typical example of the reaction product is a water soluble salt of a substituted succinic acid more precisely a water soluble salt of an alkenylsuccinic anhydride such as octenyl succinic anhydride dodecenyl succinic anhydride and the like the synthetic sizing agents are described in more detail in japanese patent publication kokoku no 565 65 in practical application of the paper sizing method of the present invention the various known processes are adopted except for adjusting the ph to the specific range and using the vinylamine polymer as a size fixing aid in papermaking process for example to an aqueous pulp slurry are added 0 05 to 2 by weight based on pulp solid of an acidic sizing agent 0 1 to 5 by weight based on pulp solid of alum and 0 005 to 0 5 by weight of the vinylamine polymer as a size fixing aid and then the conventional papermaking method is applied while adjusting the ph to the range from 5 5 to 7 5 the order of the addition is not otherwise limited usually a sizing agent and alum are added to a pulp slurry and then a size fixing aid is added thereto the kinds of pulps are not particularly limited and various known pulps may be used optionally pulps may include ground pulp semi ground pulp sulfite pulp semi.