<p>Measuring clock skew of devices over a network fully relies on the offsets, the differences between sending and receiving times. Offsets that shape a thick line are the most ideal one as their slope is directly the clock skew sought. When some outliers separate from the thick line due to higher delay jitter, current advanced approaches use the lower bound or the majority of offsets to derive accurate clock skew. However, outliers in offsets that shape parallel dotted lines, reduce the availability of offsets in the lower region, and scatter widely the offsets from their majority zone. These conditions drive the current skew estimation approaches to lose their accuracy. This paper then developed a new method, which reconstructs back the outliers into their origin positions, in order to provide ideal offsets for clock skew measurement. The experimental evaluations have demonstrated that the clock skew accuracy of dotted-lines offsets tampered by outliers was improved from 2.1 to 0.9 ppm by the proposed reconstruction method. For a broader purpose, the reconstruction method has been adjusted to be implemented also on non-dotted-lines offsets. The robustness of the proposed method for this case has also been exhibited by the very ideal reconstructed offsets that shape like a thick line.</p>