diff --git a/src/MultivariateBases.jl b/src/MultivariateBases.jl
index b3104a4..098fc7a 100644
--- a/src/MultivariateBases.jl
+++ b/src/MultivariateBases.jl
@@ -16,7 +16,7 @@ end
 Variables{B}(vars) where {B} = Variables{B,typeof(vars)}(vars)
 
 function Base.one(v::Variables)
-    return MP.monomial(v.variables, constant_monomial_exponents(v))
+    return Polynomial(v, constant_monomial_exponents(v))
 end
 
 function variable_index(v::Variables, var)
diff --git a/test/monomial.jl b/test/monomial.jl
index cd24a10..1781b7e 100644
--- a/test/monomial.jl
+++ b/test/monomial.jl
@@ -14,6 +14,8 @@ function test_monomial(x, y)
         @test vars(exponents(x^3)) != vars(exponents(x^2))
         o = vars(exponents(constant_monomial(x^2)))
         @test isone(o)
+        @test one(vars) isa MB.Polynomial
+        @test isone(one(vars))
         vars2 = MB.Variables{MB.Monomial}(_copy(variables(x)))
         @test vars == vars2
         @test hash(vars) == hash(vars2)
@@ -150,6 +152,7 @@ function test_monomial(x, y)
 
     @testset "constant_algebra_element ordering" begin
         ce = MB.constant_algebra_element(full, Float64)
+        @test isone(ce)
         keys, vals = test_graded_order(ce)
         @test keys == [e_00]
         @test vals == [1.0]