  We present a method to measure the CKM phase $\alpha$ and the tree and
penguin (strong and electroweak) amplitudes in $B \rightarrow \pi \pi$ decays,
based on isospin consideration and the weak assumption that all tree amplitudes
have a common strong phase and all penguin amplitudes have a different common
phase. The method needs only the time-independent measurements of the relevant
decay rates in $B \rightarrow \pi \pi$. We also propose a method to
experimentally examine the validity of the assumption that all penguin
amplitudes have the same strong phases, and to extract detailed informations
about the hadronic matrix elements.
