It is often necessary to compare two measurement methods in medicine and other experimental sciences. This problem covers a broad range of data with applications arising from many different fields. The Bland-Altman method has been a favorite method for concordance assessment. However, the Bland-Altman approach creates a problem of interpretation for many applications when a mixture of fixed bias, proportional bias and/or proportional error occurs. In this paper, an improved Bland-Altman method is proposed to handle more complicated scenarios in practice. This new approach includes Bland-Altman's approach as its special case. We evaluate concordance by defining an agreement interval for each individual paired observation and assessing the overall concordance. The proposed interval approach is very informative and offers many advantages over existing approaches. Data sets are used to demonstrate the advantages of the new method.