Systematic sampling is one of the simplest and popular methods for selecting a random sample from a finite population. The diagonal systematic sampling scheme is a type of systematic sampling design which has gained the attention of researchers during the last two decades. In this paper, a modification to the conventional diagonal systematic sampling design is proposed for use in situations where population units follow a linear trend. It is found that the proposed strategy reduces the variance of the diagonal systematic sampling thus resulting in an efficient sampling design. The mathematical conditions under which the suggested modified diagonal systematic sampling design is more precise than some of the available sampling designs are derived. With the help of a numerical illustration using milk yield data, it is shown that the proposed sampling scheme is more efficient than some of the available sampling schemes.