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Webster 1913 Edition

(ĭrˊrē̍-spĕk′tĭv-ly̆)

adv.

Without regard to conditions; not taking circumstances into consideration.

Prosperity, considered absolutely and

irrespectively

, is better and more desirable than adversity.

South.

adv.

Without regard to circumstances, or not taking them into consideration.

irrespectively ‎(comparative more irrespectively, superlative most irrespectively)

In an irrespective manner.
Without regard to conditions; not making circumstances into consideration.
- 2003, Patrick Bonin, chapter 8, in Mental Lexicon: Some Words to Talk About Words, ISBN 1590338405, page 175:
  This suggests that consistency plays a role irrespectively of frequency.