Summary: For an edge coloring of a connected graph \(G\) of order 3 or more with positive integers, the chromatic mean of a vertex \(v\) of \(G\) is defined as that vertex color which is the average of the colors of the edges incident with \(v\). Only those edge colorings \(c\) for which the chromatic mean of every vertex is a positive integer are considered. If distinct vertices have distinct chromatic means, then \(c\) is called a rainbow mean coloring of \(G\). The maximum vertex color in a rainbow mean coloring \(c\) of \(G\) is the rainbow mean index of \(c\), while the rainbow mean index of \(G\) is the minimum rainbow mean index among all rainbow mean colorings of \(G\). In this note, we prove that every path \(P_n\) of order \(n\geq 3\) has rainbow mean index \(n\) except \(P_4\) which has rainbow mean index \(5\).