Add to ORKGIn this paper, we consider a new form of the arithmetic mean method for solving large block tridiagonal linear systems. The iterative method converges for systems with coefficient matrices that are symmetric positive definite or positive real or irreducible L-matrices with a strong diagonal dominance. When the coefficient matrix is symmetric positive definite, an additive preconditioner for the conjugate gradient method is derived. Both the iterative method and the preconditioner are very suitable for parallel implementation on a multivector computer. Some numerical experiments on systems resulting from the discretization of an elliptic partial differential equation are carried out on the Cray Y-M