diff --git a/examples/taumethod.jl b/examples/taumethod.jl
new file mode 100644
index 0000000..d793237
--- /dev/null
+++ b/examples/taumethod.jl
@@ -0,0 +1,26 @@
+using ClassicalOrthogonalPolynomials
+
+T = ChebyshevT()
+C⁴ = Ultraspherical(4)
+
+n = 20 # truncation size
+R  = (C⁴\T)[1:n,1:n] # discretization of I
+D¹ = (C⁴\diff(T))[1:n,1:n]
+D⁴ = (C⁴\diff(T,4))[1:n,1:n]
+γ₀ = T[[begin,end],1:n]
+γ₁ = diff(T)[[begin,end],1:n]
+
+φ₁ = (C⁴\T)[1:n,n-1]
+φ₂ = (C⁴\T)[1:n,n]
+
+Z = zeros(2,n)
+𝐳₂ = zeros(2)
+𝐳 = zeros(n)
+
+A = [γ₀     Z       Z       𝐳₂   𝐳₂;
+     Z      γ₀      Z       𝐳₂   𝐳₂;
+     γ₁     Z       Z       𝐳₂   𝐳₂;
+     Z      γ₁      Z       𝐳₂   𝐳₂;
+     R      -D¹     0I      𝐳   𝐳;
+     D⁴     0I      R       𝐳   𝐳;
+     0I     D⁴      D¹      φ₁  φ₂]
\ No newline at end of file