By using a SISAM spectrometer with a 0.03 cm−1 resolving power we have measured the line-strengths for the 4 ← 0 and 5 ← 0 absorption bands of the HI molecule. The pressure in the White cell was important enough to assume the lines to be described through a Lorentz profile, and we have used the 'curve of growth' method. By using all the available data on the 1 ← 0,2 ← 0, and 3 ← 0 bands, we have calculated the first six coefficients of the dipole moment expansion series. The shape of the experimental dipole moment function shows that the HI bond is primarily covalent.