A key predistribution scheme for Wireless Sensor Networks was proposed by Choi and Youn in 2005, which is based on LU decomposition of symmetric matrix. After that, several key predistribution schemes were designed on the basis of Choi and Youn's original scheme. In this paper, we carefully investigate a mathematical theorem about symmetric matrix, by following which adversaries could easily obtain the secret keys deployed via Choi and Youn's scheme. We also analyze all the schemes derived from Choi and Youn's and point out their vulnerabilities. In addition, we propose a revised scheme avoiding the security flaw.