Theoretical proof for the existence of cooperativity (experimental evidences have already been reported in our earlier work: Biochem. Biophys. Res. Commun., 293 (2002) 870) in the phenomenon of DNA renaturation has been obtained using a generalized birth-death master equation approach. Results have shown that no special searching mechanism (i.e. a facilitated mechanism) was necessary for complementary DNA strands to find their correct-contacts but searching by a 'random jump' method was enough to explain not only the observed cooperativity phenomenon but also the magnitude of correct-contact-forming rate constant. Impact of cooperativity phenomenon on length of primers and their specificity in polymerase chain reaction has also been discussed.