Key management is an important area of research in Wireless Sensor Networks (WSN), because resource constraints make security protocols difficult to be implemented. Key predistribution, which involves preloading keys in sensor nodes, has been considered as the best solution when sensor nodes are battery powered and have to work unattended. We propose a deterministic key predistribution scheme in WSN, in which sensor nodes are deployed randomly. This scheme relies on affine planes for key predistribution. Our scheme offers a better security to node compromise, than other deterministic predistribution schemes. Our scheme has the same storage requirements as other predistribution schemes for large networks of thousands of nodes. We also show that our scheme performs better than non deterministic schemes when communication overheads are considered.