  We show that, due to the Dzyaloshinskii-Moriya and the XY anisotropies, the
disordered diagonal spin spiral in the insulating La$_{2-x}$Sr$_x$CuO$_4$
generates a diagonal charge density wave (CDW) with the wave vector twice of
that of the spin spiral. The amplitude of the CDW depends on values of the
anisotropies, the doping level, and on the density of states at the chemical
potential. Based on available experimental data we estimate that for 4% doping
the amplitude of CDW is about 1/10 of the doping level. We believe that this
mechanism explains the CDW observed recently in Zn-codoped detwinned
La$_{2-x}$Sr$_x$CuO$_4$.
