Hydrogels based on chitosan are very versatile materials which can be used for tissue engineering as well as in controlled drug delivery systems. One of the methods for obtaining a chitosan-based hydrogel is crosslinking by applying different components. The objective of the present study was to obtain a series of new crosslinked chitosan-based films by means of solvent casting method. Squaric acid—3,4-dihydroxy-3-cyclobutene-1,2-dione—was used as a safe crosslinking agent. The effect of the squaric acid on the structural, mechanical, thermal, and swelling properties of the formed films was determined. It was established that the addition of the squaric acid significantly improved Young’s modulus, tensile strength, and thermal stability of the obtained materials. Moreover, it should be stressed that the samples consisting of chitosan and squaric acid were characterized by a higher swelling than pure chitosan. The detailed characterization proved that squaric acid could be used as a new effective crosslinking agent.