A test of exponentiality of Kolmogorov-Smirnov type based on a simplified variant of loss-of-memory property and proposed by Angus [3] is considered. We find corresponding large-deviation asymptotics under the null-hypothesis reducing the problem to large deviations of U-statistics with a special kernel. As a corollary, Bahadur local efficiency of Angus test is calculated for most commonly used parametric alternatives to exponentiality.