Density fingering of the chlorite-tetrathionate reaction is studied experimentally in a Hele-Shaw cell. It is shown that the dispersion curve describing the linear regime of the evolution of pattern formation is strongly affected by the orientation of the cell. Both the growth rate and the range of wave numbers associated with the unstable modes decrease on increasing the tilt angle from the vertical. From the dispersion curves, the dependence of the most unstable mode on the tilt angle is determined experimentally and compared with that of existing theories. The ratio of the marginal wave number, separating the stable and unstable modes, to the wave number with the maximum growth rate indicates that the high-frequency disturbances are stabilized by the diffusion of the components in the reaction.