For a set of nonnegative integers S let R S (n) denote the number of unordered representations of the integer n as the sum of two different terms from S. In this paper we focus on partitions of the natural numbers into two sets affording identical representation functions. We solve a recent problem of Lev and Chen.2000 AMS Mathematics subject classification number : 11B34. Key words and phrases: additive number theory, representation functions, partitions of the set of natural numbers.