  Intracellular positive ions neutralise negative charges on the phosphates of
a DNA strand conferring greater strength on the hydrogen bonds that connect
complementary strands into a double helix and so confer enhanced stability.
Beyond a certain value of salt concentration, the DNA molecule displays a
unstable nature {\it in vivo} as well as {\it in vitro}. We consider a wide
range of salt concentrations and study the stability of the DNA double helix
using a statistical model. Through numerical calculations we attempt to explain
the different behaviour exhibited by DNA molecules in this range. We compare
our results with experimental data and find a close agreement.
