We present the study of the correlation properties of RBC flickering using double-path interferometric quantitative phase microscopy (QPM) using detrended fluctuation analysis (DFA). For DFA of RBC membrane fluctuations, we have measured time series thickness variations of a normal RBC for 20 seconds. The amplitude of membrane fluctuations in RBC have showed significantly larger than the background noise level without a RBC. We have demonstrated a practical DFA application for QPM by studying the correlation property of RBC membrane fluctuations in a noninvasive manner. By measuring the fractal scaling exponents of the time series RBC thickness variations obtained from QPM, we have analyzed the correlation properties of RBC membrane fluctuations and the background noise without a sample. The exponents for a normal RBC revealed the long-range correlation property in time series during 20 seconds. However, the averaged exponent for background noise outside a cell was close to the exponent of white noise.