令M₁为一个有限的von Neumann代数，τ₁为其上的一个忠实正规迹态. 我们将证明，如果M₁中存在一列两两正交的酉元列{u_k：k∈N}，则对任意具有忠实正规迹态τ₂的有限vonNeumann代数 M₂ （≠C），迹自由积（M₁，τ₁） * （M₂，τ₂） 是Ⅱ₁型因子.作为推论可以得出，如果M₁有一个von Neumann子代数N不包含最小投影，则对任意具有忠实迹态τ₂的有限von Neumann代数M₂（≠C），迹自由积（M₁，τ₁）*（M₂，τ₂）是Ⅱ₁型因子.

Let M₁ be a finite von Neumann algebra with a faithful normal trace τ₁ and let M₁^o={a ∈ M,τ₁(a)=0}. We prove that, if there is a sequence {u_k:k ∈ M } of orthogonal unitaries in M₁^o, then for any finite von Neumann algebra M₂(≠C) with a faithful normal trace τ₂, the tracial free product (M₁, τ₁) * (M₂, τ₂) is a type Ⅱ₁ factor. As a corollary, we obtain that, if there is a von Neumann subalgebra N of M₁ such that N has no minimal projection, then for any finite von Neumann algebra M₂(≠ C) with a faithful normal trace τ₂, the tracial free product (M¹, τ₁) * (M₂, τ₂) is a type Ⅱ₁ factor.