We present the first statistical study of the anisotropy of the magnetic field turbulence in the solar wind between 1 and 200 Hz, i.e., from proton to sub-electron scales. We consider 93 ten-minute intervals of the Cluster/STAFF measurements. We find that the fluctuations $\delta {B}_{\perp }^{2}$ are not gyrotropic at a given frequency f, a property already observed at larger scales ($\parallel /\perp $ means parallel/perpendicular to the average magnetic ${{\boldsymbol{B}}}_{0}$). This non-gyrotropy gives indications of the angular distribution of the wave vectors ${\boldsymbol{k}}$: at $f\lt $ 10 Hz, we find that ${k}_{\perp }\gg {k}_{\parallel }$, mainly in the fast wind; at $f\,\gt $ 10 Hz, fluctuations with a non-negligible k ∥ are also present. We then consider the anisotropy ratio $\delta {B}_{\parallel }^{2}/\delta {B}_{\perp }^{2}$, which is a measure of the magnetic compressibility of the fluctuations. This ratio, always smaller than 1, increases with f. It reaches a value showing that the fluctuations are more or less isotropic at electron scales, for $f\geqslant 50\,\mathrm{Hz}$. From 1 to 15–20 Hz, there is a strong correlation between the observed compressibility and the one expected for the kinetic Alfvén waves (KAWs), which only depends on the total plasma β. For $f\gt 15\mbox{--}20\,\mathrm{Hz}$, the observed compressibility is larger than expected for KAWs, and it is stronger in the slow wind: this could be an indication of the presence of a slow-ion acoustic mode of fluctuations, which is more compressive and is favored by the larger values of the electron to proton temperature ratio generally observed in the slow wind.