If you use an empty cuvette as reference its transmissivity can be lower than that of the filled cuvette, and therefore you can get negative absorbance (filled cuvette transmitting more than reference arm). This is however a spurious effect due to reflection on the cuvette walls. For the empty cuvette each wall contributes two reflecting surfaces, with air-glass interface. For the filled cuvette the inner surface of the wall in in contact with water, resulting in lower reflectivity due to lower (glass-water) refractive index mismatch. I think you should never get negative absorbance, if you properly account for reflectivity.

If you are after water absorption, the cuvette you use fro the baseline recording should be completely dry. Then, the absorbance of water is not so strong so it might be difficlult to record in a standard 1-cm cuvette, You may try i) cuvettes with a longer pathlength e.g. 5 cm; ii) increase the signal integration time if your spectrophotometer will allow you to do this (generally it is called response time). 

If you use an empty cuvette as reference its transmissivity can be lower than that of the filled cuvette, and therefore you can get negative absorbance (filled cuvette transmitting more than reference arm). This is however a spurious effect due to reflection on the cuvette walls. For the empty cuvette each wall contributes two reflecting surfaces, with air-glass interface. For the filled cuvette the inner surface of the wall in in contact with water, resulting in lower reflectivity due to lower (glass-water) refractive index mismatch. I think you should never get negative absorbance, if you properly account for reflectivity.

Negative absorbance would indicate that the water or other material is releasing photons in response to being immuminated. That is it would be lasing or releasing energy from a metastable state, both of which are unlikely for liquid water.

If you absorbance as measured is going lower than zero, you have a background subtraction error or another optical effect. Running a blank with an empty cell is not good practice as it will have losses due to different surface reflections in the absence of water.

There are spectra of water available from a number of sources which you can look up.

Mauro Falconieri is right. The amount depends on the refractive indices at the surface, i.e., the glass and the air/the water. The loss of transmission increases with difference between the two refractive indices. In the UV up to 5% loss per surface can occur between quartz and air.

I agree fully with the answers of my colleagues.  Please note that we always need more infos for a good answer:

The method with an empty cuvette is not good !!

What a kind of cuvettes and what a sample of  water are you measuring?

Have you quartz cvettes(Please give specification of them/ Company, Cutoff ....). For your measures you must have very clean cuvettes. If you use cuvettes of a colleague, clean please them with sulfuric acid and  wash them with bidist. water until you have no traces of the acid before use. (Some drugs or dyes adsorb very strongly on quartz).

Are you using single or dual beam spectrometer. This aspect is not clear in your question!

If you use dual beam spectrometer, please test the lamps and mirror and slit. Old lamps give always bad results.

Your cuvettes must be closed with teflon plug and you must have the same water quantity in every cuvette.

Thank you for your answer.

I think you use a glass cylinder for water. it focus light into detector. use a cubic glass for your water which don't focus light.

The answer of Mauro Falconieri and others are correct. The method is to compare your water solution with pure, distileter, deioniseted one. The absorption of clear water that is putted in the reference branch you can find somewhere. You have to compare you real water with ideal reference. The measurement result will be positive don't worry.

Thank you for all advices and suggestions. I manage to get positive value following @Aurelian Popescu advise. 

Another possibility, although rather unlikely, is that water under test is contaminated with glowing  radioactive or phosphorescent species which emit light into the sample path. To detect this,  instrument sensitivity has to be unusually high though! 

The answer of Aleksandr is related to my answer. Please give morfe infos about your measured water!!!

JRG

Indeed, the reference measurement for a neat sample can never be an empty cuvette. The reason is indeed related to reflection, but a little bit more complex, as you have to take into account that light is reflected back and forth. A more detailed explanation can be found in https://www.researchgate.net/publication/298908902_Employing_Theories_Far_beyond_Their_Limits-The_Case_of_the_Boguer-_Beer-Lambert_Law