The Steiner tree problem is to nd a shortest subgraph
that spans a given set of vertices in a graph. This problem
is known to be NP-hard and it is well known that a polynomial time
2-approximation algorithm exists. In 1996 Zelikovsky [11] suggested
an approximation algorithm for the Steiner tree problem that is called
the relative greedy algorithm. Till today the performance ratio of this
algorithm is not known. Zelikovsky provided 1.694 as an upper bound
and Gröpl, Hougardy, Nierho and Prömel [6] proved that 1.333 is a
lower bound. In this paper we improve the lower bound for the performance
ratio of the relative greedy algorithm to 1.385.