We report the result of a study in which we have used very deep broadband V and I WFPC2 images of the R136 cluster in the Large Magellanic Cloud from the HST archive , to sample the luminosity function below the detection limit of 2.8 M _ { \odot } previously reached . In these new deeper images , we detect stars down to a limiting magnitude of m _ { F 555 W } = 24.7 ( \simeq 1 magnitude deeper than previous works ) , and identify a population of red stars evenly distributed in the surrounding of the R136 cluster . A comparison of our color-magnitude diagram with recentely computed evolutionary tracks indicates that these red objects are pre-main sequence stars in the mass range 0.6 - 3 M _ { \odot } . We construct the initial mass function ( IMF ) in the 1.35 - 6.5 M _ { \odot } range and find that , after correcting for incompleteness , the IMF shows a definite flattening below \simeq 2 M _ { \odot } . We discuss the implications of this result for the R136 cluster and for our understanding of starburst galaxies formation and evolution in general .