The absorbance can only take positive values. It is defined as the logarithm (base 10) of the quotient between incident and transmitted light intensities (Io/It). If a negative value were obtained, that would  imply that the argument of the log function, in this case (Io/It), would be less than 1. For that case, the incident light intensity is less than the transmitted light intensity.

My conclusion is that the light signal that the spectrophotometer is detecting comes from a process different from light absorption.

Regarding the calculation of a concentration from absorbance values, this can only be performed from Lambert-Beer law, strictly for positive absorbance values.

Adela's physics is fine.

But in setting up the instrument you may have set zero absorbance, e.g. on a reagent blank that has some absorbance.

Then you perhaps fitted a curve to your calibration data. And even though the r square value may be 0.99 this does not mean that the line fits the data well at low absorbances.

In this combination of circumstances it is indeed possible to measure a negative absorbance and for the calibration equation to predict a positive concentration.

I agree with Adela  that you are dealing with an artifact

I think this link is very useful, 

http://www.instanano.com/characterization/theoretical/concentration-calculation-from-uv-vis-absorbance/

Thank you all for your contributions.

they are helpful.

Thank you all for your contributions.

they are helpful.