Roughly speaking, the author shows that the \(r\)-th order jets can be characterized as homomorphic images of germs of smooth maps. – More precisely, let us denote by \(G(M,N)\) the set of all germs of smooth maps \(M\to N\). Consider a rule \(F\) transforming every pair \((M,N)\) of manifolds into a fibered manifold \(F(M,N)\) over \(M\times N\) and a system \(\varphi\) of maps \(\varphi_{M,N}:G(M,N)\to F(M,N)\) commuting with the projections \(G(M,N)\to M\times N\) and \(F(M,N)\to M\times N\). Under some quite natural requirements (“surjetiveness”, “composability”, “regularity”, “product property”), it is proved that there exists \(r\in\mathbb{N}\) such that \((F,\varphi)=(J^ r,j^ r)\), where \(J^ r\) is the \(r\)-th order jet functor and \(j^ r(\text{germ}_ xf):=j^ r_ xf\). The geometric meaning of the product property is also clarified.