The classical Lipschitz-type criteria guarantee unique solvability of the scalar initial value problem ẋ = f (t, x), x(t₀) = x₀, by putting restrictions on |f (t, x) - f (t, y)| in dependence of |x - y|. Geometrically it means that the field differences are estimated in the direction of the x-axis. In 1989, Stettner and the second author could establish a generalized Lipschitz condition in both arguments by showing that the field differences can be measured in a suitably chosen direction v = (d_t, d_x), provided that it does not coincide with the directional vector (1, f (t₀, x₀)). Considering the vector v depending on t, a new general uniqueness result is derived and a short proof based on the implicit function theorem is developed. The advantage of the new criterion is shown by an example. A comparison with known results is given as well.