diff --git a/stdlib/LinearAlgebra/test/lapack.jl b/stdlib/LinearAlgebra/test/lapack.jl
index dfcf3c89dac2a..d1130072573ec 100644
--- a/stdlib/LinearAlgebra/test/lapack.jl
+++ b/stdlib/LinearAlgebra/test/lapack.jl
@@ -196,7 +196,8 @@ end
 
 @testset "gebal/gebak" begin
     @testset for elty in (Float32, Float64, ComplexF32, ComplexF64)
-        A = rand(elty,10,10) * Diagonal(exp10.(range(-10, stop=10, length=10)))
+        typescale = log10(eps(real(elty))) / 3 * 2
+        A = rand(elty,10,10) * Diagonal(exp10.(range(typescale, stop=-typescale, length=10)))
         B = copy(A)
         ilo, ihi, scale = LAPACK.gebal!('S',B)
         Bvs = eigvecs(B)