The Collaborative International Dictionary of English v.0.48:

Linnaean \Lin*n[ae]"an\, Linnean \Lin*ne"an\ (l[i^]n*n[=e]"an),
   prop. a.
   Of or pertaining to Linn[ae]us, the celebrated Swedish
   botanist.
   [1913 Webster]

   Linnaean system, Linnean system (Bot.), the system in
      which the classes of plants are founded mainly upon the
      number of stamens, and the orders upon the pistils; the
      artificial or sexual system.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Linnaean
    adj 1: of or relating to Linnaeus or to the system of taxonomic
           classification that Linnaeus proposed [syn: Linnaean,
           Linnean]