In this paper, a non-classical autocorrelation detector adopting a newly defined test statistic is introduced to solve the typical problem of detecting a narrowband signal transmitted over an additive white Gaussian noise (AWGN) channel. Error probability analyses are performed for a noncoherent frequency-shift-keying (FSK) system employing the proposed test-statistic. Through the histogram approach, the probability density functions of the test-statistics are plotted to explain the analysis model. All numerical results obtained indicate the limited improvement in error performance under the lower signal-to-noise ratio (SNR) and the use of higher number of samples per bit will finally provide the almost same confident potential of improvement in error rate as the system using matched filters (MFs) gives.