Source : Webster's Revised Unabridged Dictionary (1913)

Uncompromising \Un*com"pro*mi`sing\, a.
   Not admitting of compromise; making no truce or concessions;
   obstinate; unyielding; inflexible. --
   {Un*com"pro*mi`sing*ly}, adv.

Source : WordNet®

uncompromisingly
     adv : in an uncompromising manner