Some short gamma-ray bursts (GRBs) are followed by longer extended emission (EE), lasting anywhere from similar to 10 to similar to 100 s. These short GRBs with EE can possess observational characteristics of both short and long GRBs (as represented by GRB 060614), and the traditional classification based on the observed duration places some of them in the long GRB class. While GRBs with EE pose a challenge to the compact-binary merger scenario, they may therefore provide an important link between short-and long-duration events. To identify the population of GRBs with EE regardless of their initial classifications, we performed a systematic search of short GRBs with EE using all available data (up to 2013 February) of both Swift/BAT and Fermi/GBM. The search identified 16 BAT and 14 GBM detected GRBs with EE, several of which are common events observed with both detectors. We investigated their spectral and temporal properties for both the spikes and the EE, and examined correlations among these parameters. Here we present the results of the systematic search as well as the properties of the identified events. Finally, their properties are also compared with short GRBs with EE observed with BATSE, identified through our previous search effort. We found several strong correlations among parameters, especially when all of the samples were combined. Based on our results, a possible progenitor scenario of two-component jet is discussed.