The contribution of order alpha (2)(Z alpha)(6)ln(3)(Z alpha)(-2) to the gr
ound-state Lamb shift in hydrogen induced by the loop-after-loop diagram is
evaluated analytically. An additional contribution of this order is found
compared to the previous calculation by Karshenboim [Sov. Phys. JETP 76, 51
1 (1993)]. As a result, agreement is achieved for this correction between d
ifferent numerical and analytical methods.