We consider wavelet decompositions of spaces of Hermite type splines of class C¹(α, β) that are defined by a 4-component vector-valued function ℓ(t) C¹ (α, β) by means of a grid X (not necessarily uniform) on (α, β) ℓ¹ (the special case ℓ(t)^def = (1, t, t²,t³) ^T corresponds to cubic Hermite splines). The basis wavelets obtained are compactly supported. The decomposition and reconstruction formulas are given. Bibliography: 8 titles.