||The frustrated spin-l/2 Heisenberg model is studied on finite clusters of sizes up to 32 sites using the Lanczos algorithm. Frustration is introduced in the model through an additional coupling between spins at two lattice constants apart ("J1- J3 model"). The study is made possible by using symmetry operations to reduce the size of the Hilbert space, and by using parallel processing on a workstation cluster. We search for novel ground state properties as the frustration changes by studying the low lying excited states, the structure factors and various order parameters. For small J3/J1, the Neel order persists. Finite-size scaling using 4x4,24-site and 32-site lattices shows that the Neel order vanishes at J3/J1 ~ 0.2 in the thermodynamic limit. For large J3/J1, we expect a state with four decoupled lattices having Neel order. At intermediate values of J3/J1, the peak of the static structure factor S(q) on the 32-site lattice shifts away from (π,π) to ([3pi/4,3pi/4]) and finally to (π/2,π/2) as J3/J1 increases. At the same time the lowest energy peak of the dynamic structure factor S(q,w) changes from (π,π) to ([3pi/4, 3pi/4]) and then to (π/2,π/2) . Also, there is an enhancement in the twist order parameter as J3/J1 increases. All of these indicate incommensurate ordering in this region of J3/J1. However, the low lying excitation energy spectrum suggests that this incommensurate order is short range and may not be stable in thermodynamic limit. In the same region, the first excited state has the symmetries of the columnar dimer state. Finite-size studies on the columnar dimer order parameter and the energy gap suggest the presence of long range columnar dimer order. Hence, this state is the best candidate for the ground state of the JI-J3 model in an intermediate J3/J1 region.