We present evidence showing that the statistical properties of turbulence in the scrape-off layer (SOL) are not modified in a high-confinement mode (H-mode) inbetween edge-localized modes (ELMs) with respect to a low confinement mode (L-mode). The plasma being in the upper-single null magnetic configuration, the reciprocating probe around the bottom X-point is used to characterize in the same discharge the low and the high-field SOL. In H-mode inbetween ELMs, the average value and the standard deviation of the ion saturation current are found very close to values in L-mode. The normalized standard deviation is found to have the same values as in L-mode independently of the probe position. The probability distribution function is found similar in the two regimes reflecting the fact that the two transport processes, diffusion and convection, are not modified with respect to each other. The power spectra were also found similar, indicating the same distribution of the turbulence intensity among the scales in L- and H-modes. The plasma profiles in the SOL, determined using the lithium beam diagnostic, were found to have the same shape as a function of the radial position also reflecting the non-modification of the transport properties in L- and H-modes.