This article investigates the value of perfect monitoring information for optimal replacement of deteriorating systems in the Proportional Hazards Model (PHM). A continuous-time Markov chain describes the condition of the system. Although the form of an optimal replacement policy for system under periodic monitoring in the PHM was developed previously, an approximation of the Markov process as constant within inspection intervals led to a counter intuitive result that less frequent monitoring could yield a replacement policy with lower average cost. This article explicitly accounts for possible state transitions between inspection epochs to remove the approximation and eliminate the cost anomaly. However, the mathematical evaluation becomes significantly more complicated. To overcome this difficulty, a new recursive procedure to obtain the parameters of the optimal replacement policy and the optimal average cost is presented. A numerical example is provided to illustrate the computational procedure and the value of condition monitoring. By taking the monitoring cost into consideration, the relationships between the unit cost of periodic monitoring and the upfront cost of continuous monitoring under which the continuous, periodic, or no monitoring scheme is optimal are obtained.