In this paper, we revisit Grid-Based Key Pre-Distribution Scheme in Wireless Sensor Network to investigate improving the connectivity of the network and maintain both the security level and communication overhead. Both of the original work and our modification are based on using symmetric bivariate polynomials for generating cryptographic keys. In addition, their work relies on the usage of multi-dimensional grid to assign the polynomials on the sensor nodes allocated on the intersections of the grid and provide a needed connectivity. In this work we consider the simplification of the key establishment logic, the enhancement of connectivity in what we call the plat polynomial assignment. We present detailed discussion on the connectivity, resources usage, and security features that shows better results on the side of the connectivity, intermediate node discovery and security measurement. Finally, we provide a comparison between our results and other existing solutions including the revisited scheme.