  We have considered the 1D dimerized frustrated antiferromagnetic
(ferromagnetic) Heisenberg model with arbitrary spin $S$. The exact classical
magnetic phase diagram at zero temperature is determined using the LK cluster
method. Cluster method results, show that the classical ground state phase
diagram of the model is very rich including first and second-order phase
transitions. In the absence of the dimerization, a second-order phase
transition occurs between antiferromagnetic (ferromagnetic) and spiral phases
at the critical frustration $\alpha_c=\pm 0.25$. In the vicinity of the
critical points $\alpha_c$, the exact classical critical exponent of the spiral
order parameter is found 1/2. In the case of dimerized chain ($\delta\neq0$),
the spiral order shows stability and exists in some part of the ground state
phase diagram. We have found two first-order critical lines in the ground state
phase diagram. These critical lines separate the antiferromagnetic from spiral
phase.
