  In the conventional spin noise spectroscopy, the probe laser light monitors
fluctuations of the spin orientation of a paramagnet revealed as fluctuations
of its gyrotropy, i.e., circular birefringence. For spins larger than 1/2,
there exists spin arrangement of a higher order---the spin alignment---which
also exhibits spontaneous fluctuations. We show theoretically and
experimentally that the alignment fluctuations manifest themselves as the noise
of the linear birefringence. In a magnetic field, the spin-alignment
fluctuations, in contrast to those of spin orientation, show up as the noise of
the probe-beam ellipticity at the double Larmor frequency, with the most
efficient geometry of its observation being the Faraday configuration with the
light propagating along the magnetic field. We have detected the spin-alignment
noise in a cesium-vapor cell probed at the wavelength of D2 line (852.35 nm).
The magnetic-field and polarization dependence of the ellipticity noise are in
full agreement with the developed theory.
