In this paper distributed storage systems with exact repair are studied. A construction for regenerating codes between the minimum storage regenerating (MSR) and the minimum bandwidth regenerating (MBR) points is given. To the best of author's knowledge, no previous construction of exact-regenerating codes between MBR and MSR points is done except in the work by Tian et al. On contrast to their work, the methods used here are elementary. In this paper it is shown that in the case that the parameters $n$, $k$, and $d$ are close to each other, the given construction is close to optimal when comparing to the known functional repair capacity. This is done by showing that when the distances of the parameters $n$, $k$, and $d$ are fixed but the actual values approach to infinity, the fraction of the performance of constructed codes with exact repair and the known capacity of codes with functional repair, approaches to one. Also a simple variation of the constructed codes with almost the same performance is given.