Intra- and inter-speaker information, which include acoustical, speaker style, speech rate and temporal variation, despite their critical importance for the verification of claims, still have not been captured effectively. As a result of such modeling deficiency, existing speaker verification systems generally test claimed utterances with interfacing procedures that are common to all speakers. In this paper, a novel method is introduced in which speaker-specific attributes are expressed with reliable, first and second order intra-speaker and inter-speaker statistical information on the output space of speaker models in an explicit way. This is achieved through the computation of the Speech Unit Confusion Matrix (SUCM) that is employed in the scoring phase. An online updating procedure of SUCM is also presented. Experimental results with spoken alphabetic characters used as the basic speech unit indicate that the new method can improve system performance significantly. The method can also be directly extended to the use of other speech units (phonemes, sub-words, digits).