In this work, we find the necessary and sufficient condition for the maximal entanglement of the state, |ψ> = μ|α>|β> + λ|α>|δ> + ρ|ϒ>|β> + ν|ϒ>|δ>, constructed by linearly independent coherent states with real parameters when <α|ϒ>=<β|δ>. To this aim we use the concurrence.