Discoveries of rotating radio transients and fast radio bursts ( FRBs ) in pulsar surveys suggest that more of such transient sources await discovery in archival data sets . Here we report on a single-pulse search for dispersed radio bursts over a wide range of Galactic latitudes ( |b| < 60 \degree ) in data previously searched for periodic sources by Burgay et al . We re-detected 20 of the 42 pulsars reported by Burgay et al . and one rotating radio transient reported by Burke-Spolaor . No FRBs were discovered in this survey . Taking into account this result , and other recent surveys at Parkes , we corrected for detection sensitivities based on the search software used in the analyses and the different backends used in these surveys and find that the all-sky FRB event rate for sources with a fluence above 4.0 Jy ms at 1.4 GHz to be { \cal R } = 4.4 ^ { +5.2 } _ { -3.1 } \times 10 ^ { 3 } FRBs day ^ { -1 } sky ^ { -1 } , where the uncertainties represent a 99 \% confidence interval . While this rate is lower than inferred from previous studies , as we demonstrate , this combined event rate is consistent with the results of all systematic FRB searches at Parkes to date and does not require the need to postulate a dearth of FRBs at intermediate latitudes .