Magnetic field structures on the solar atmosphere are not symmetric distribution in the northern and southern hemispheres, which is an important aspect of quasi-cyclical evolution of magnetic activity indicators that are related to solar dynamo theories. Three standard analysis techniques are applied to analyze the hemispheric coupling (north-south asymmetry and phase asynchrony) of monthly averaged values of solar Ha flare activity over the past 49 years (from 1966 January to 2014 December). The prominent results are as follows: (1) from a global point of view, solar Ha flare activity on both hemispheres are strongly correlated with each other, but the northern hemisphere precedes the southern one with a phase shift of 7 months; (2) the long-range persistence indeed exists in solar Ha flare activity, but the dynamical complexities in the two hemispheres are not identical; (3) the prominent periodicities of Ha flare activity are 17 years full-disk activity cycle and 11 years Schwabe solar cycle, but the short-and mid-term periodicities cannot determined by monthly time series; (4) by comparing the non-parametric rescaling behavior on a point-by-point basis, the hemispheric asynchrony of solar Ha flare activity are estimated to be ranging from several months to tens of months with an average value of 8.7 months. The analysis results could promote our knowledge on the long-range persistence, the quasi-periodic variation, and the hemispheric asynchrony of solar Ha flare activity on both hemispheres, and possibly provide valuable information for the hemispheric interrelation of solar magnetic activity.