Source : Webster's Revised Unabridged Dictionary (1913)

Inconsequential \In*con`se*quen"tial\, a.
   Not regularly following from the premises; hence, irrelevant;
   unimportant; of no consequence. --Chesterfield. --
   {In*con`se*quen"tial*ly}, adv.

Source : WordNet®

inconsequential
     adj 1: lacking worth or importance; "his work seems trivial and
            inconsequential"; "the quite inconsequent fellow was
            managed like a puppet" [syn: {inconsequent}]
     2: not following logically as a consequence