Two instabilities could take place in plasma with a bi-Maxwellian proton distribution function with Tp∥>Tp⊥, where Tp∥ and Tp⊥ are proton temperatures, parallel and perpendicular, respectively, to the background magnetic field. The first instability is the fire hose (or whistler fire hose), generating low-frequency whistler waves at parallel propagation. We found a new, second instability, the Alfv¿n fire hose, that generates zero-frequency waves of the Alfv¿n branch at strongly oblique propagation. The Alfv¿n fire hose has a linear growth rate comparable to or even greater than that of the whistler fire hose. The two instabilities with the same initial plasma parameters are examined via one-dimensional hybrid simulations and turn out to have behavior very different from each other. The whistler fire hose has an overall quasi-linear evolution, while the evolution of the Alfv¿n fire hose is more complicated: Initially, unstable zero-frequency waves are gradually transformed into propagating Alfv¿n waves; during this process the waves are strongly damped and heat protons in a perpendicular direction. Consequently, the Alfv¿n fire hose is very efficient at destroying proton anisotropy. ¿ 2000 American Geophysical Union