The philosophy of multisplitting methods is the replacement of a large-scale linear or nonlinear problem by a set of smaller subproblems, each of which can be solved locally and independently in parallel by taking advantage of well-tested sequential algorithms. Because of this formulation most compute-intensive operations can be calculated independently and the algorithms are highly parallel. In continuation of our earlier work we utilize a new parameter-free formulation of linearly constrained convex minimization problems to obtain a parallel algorithm of multisplitting type. Numerical results both serial and parallel are reported which demonstrate its efficiency and which also show that it compares favorably to our earlier parameter-dependent approach.