The Collaborative International Dictionary of English v.0.48:

Independently \In`de*pend"ent*ly\, adv.
   In an independent manner; without control.
   [1913 Webster]

WordNet (r) 3.0 (2006):

independently
    adv 1: on your own; without outside help; "the children worked
           on the project independently"
    2: apart from others; "the clothes were hung severally" [syn:
       independently, severally]

Moby Thesaurus II by Grady Ward, 1.0:

21 Moby Thesaurus words for "independently":
   alone, by choice, electively, en grand seigneur, erectly, freely,
   gratuitously, individually, like a lord, optionally, pridefully,
   proudly, self-confidently, self-reliantly, self-respectingly,
   spontaneously, voluntarily, willfully, with head erect, with pride,
   without coercion