This paper proposes a new monitoring path design paradigm for independent dual link failures. Specifically, the new approach exploits the sequential arrival and departure property of independent failure events to uniquely localize failed links. Such property, however, cannot be captured by the existing approach, which is built upon the notion of shared risk link groups. Consequently, we show via solution space comparison that the existing approach can result in overdesign in terms of monitoring resources required. Numerical results further indicate that the new approach outperforms the existing one in terms of monitoring cost and computational efficiency.