This paper considers the problem of detecting a QPSK communication signal on carrier. We propose a method to perform the detection thanks to second order cyclostationarity theory. It is well known that for such a signal, there is no cyclic frequency multiple of the studied signal carrier frequency. Hence, the basic method of second order cyclic-moments energy measurement is unable to detect any energy directly linked to the signal carrier. In this article, we propose a novel criterion based on second order cyclic-moments that exploits the convergence speed of the cyclic autocorrelation function estimator. We show that for a modulated QPSK signal the cyclic-correlation converges to zero but not in the same way if the cyclic frequency is a multiple of the carrier frequency or not. We develop a statistical test and derive the asymptotic probability density function of the criterion to propose a detection threshold. System performance simulation results are then evaluated by Monte Carlo simulations and compared to the results of fourth order nonlinear transformation method.