We report a novel and facile method for measuring edge tensions of lipid membranes. The approach is based on electroporation of giant unilamellar vesicles and analysis of the pore closure dynamics. We applied this method to evaluate the edge tension in membranes with four different compositions: egg phosphatidylcholine (eggPC), dioleoylphosphatidylcholine (DOPC), and mixtures of DOPC with cholesterol and dioleoylphosphatidylethanolamine. Our data confirm previous results for eggPC and DOPC. The addition of 17 mol % cholesterol to the DOPC membrane causes an increase in the membrane edge tension. On the contrary, when the same fraction of dioleoylphosphatidylethanolamine is added to the membrane, a decrease in the edge tension is observed, which is an unexpected result considering the inverted-cone shape geometry of the molecule. It is presumed that interlipid hydrogen bonding is the origin of this behavior. Furthermore, cholesterol was found to lower the lysis tension of DOPC bilayers. This behavior differs from that observed on bilayers made of stearoyloleoylphosphatidylcholine, suggesting that cholesterol influences the membrane mechanical stability in a lipid-specific manner.