The problem of retargeting a larger image in a small display is to maintain recognizability of the objects. The retargeting scheme proposed in this paper provides a suitable solution to this. The input image is partitioned into rectangular strips such that alternate strips contain important or unimportant objects. Each of these rectangular strips shrinks in size to fit the entire image into the small display. Strips containing unimportant objects shrink at a higher rate than those containing important objects. It is experimentally found that this scheme performs better than many existing schemes. An estimate for the range of values for shrinkage controlling parameters is also attempted here.