  Using the high-resolution spectrometer SPI on board the International
Gamma-Ray Astrophysics Laboratory (INTEGRAL), we search for a spectral line
produced by a dark matter(DM) particle with a mass in the range 40keV < M_DM <
14MeV, decaying in the DM halo of the Milky Way. To distinguish the DM decay
line from numerous instrumental lines found in the SPI background spectrum, we
study the dependence of the intensity of the line signal on the offset of the
SPI pointing from the direction toward the Galactic Centre. After a critical
analysis of the uncertainties of the DM density profile in the inner Galaxy, we
find that the intensity of the DM decay line should decrease by at least a
factor of 3 when the offset from the Galactic Centre increases from 0 to 180
degrees. We find that such a pronounced variation of the line flux across the
sky is not observed for any line, detected with a significance higher than 3
sigma in the SPI background spectrum. Possible DM decay origin is not ruled out
only for the unidentified spectral lines, having low (~3 sigma) significance or
coinciding in position with the instrumental ones. In the energy interval from
20 keV to 7 MeV, we derive restrictions on the DM decay line flux, implied by
the (non-)detection of the DM decay line. For a particular DM candidate, the
sterile neutrino of mass MDM, we derive a bound on the mixing angle.
