The solution of the generalized Abel integral equation \[ g ( t ) = ∫ 0 t { k ( t , s ) / ( t − s ) α } f ( s ) d s , 0 > α > 1 , g(t) = \int _0^t {\{ k(t,s)/{{(t - s)}^\alpha }\} f(s)} ds,\;0 > \alpha > 1, \] where k ( t , s ) k(t,s) is continuous, by the product integration analogue of the trapezoidal method is examined. It is shown that this method has order two convergence for α ∈ [ α 1 , 1 ) \alpha \in [{\alpha _1},1) with α 1 ≑ 0.2117 {\alpha _1} \doteqdot 0.2117 . This interval contains the important case α = 1 2 \alpha = \tfrac {1}{2} . Convergence of order two for α ∈ ( 0 , α 1 ) \alpha \in (0,{\alpha _1}) is discussed and illustrated numerically. The possibility of constructing higher order methods is illustrated with an example.