Abstract Roughly speaking, the regular subspace of a Dirichlet form is also a regular Dirichlet form on the same state space. It inherits the same form of the original Dirichlet form but possesses a smaller domain. What we are concerned in this paper are the regular subspaces of associated Dirichlet forms of skew product diffusions. A skew product diffusion X is a symmetric Markov process on the product state space E 1 × E 2 ${E_{1}\times E_{2}}$ and expressed as X t = ( X t 1 , X A t 2 ) , t ≥ 0 , $X_{t}=(X^{1}_{t},X^{2}_{A_{t}}),\quad t\geq 0,$ where X i ${X^{i}}$ is a symmetric diffusion on E i ${E_{i}}$ for i = 1 , 2 ${i=1,2}$ , and A is a positive continuous additive functional of X 1 ${X^{1}}$ . One of our main results indicates that any skew product type regular subspace of X, say Y t = ( Y t 1 , Y A ~ t 2 ) , t ≥ 0 , $Y_{t}=(Y^{1}_{t},{Y^{2}_{\tilde{A}_{t}}}),\quad t\geq 0,$ can be characterized as follows: the associated smooth measure of A ~ ${\tilde{A}}$ is equal to that of A, and Y i ${Y^{i}}$ corresponds to a regular subspace of X i ${X^{i}}$ for i = 1 , 2 ${i=1,2}$ . Furthermore, we shall make some discussions on rotationally invariant diffusions on ℝ d ∖ { } ${\mathbb{R}^{d}\setminus\{{\mathbf{0}}\}}$ , which are special skew product diffusions on ( 0 , ∞ ) × S d - 1 ${(0,\infty)\times S^{d-1}}$ . Our main purpose is to extend a regular subspace of rotationally invariant diffusion on ℝ d ∖ { } ${\mathbb{R}^{d}\setminus\{{\mathbf{0}}\}}$ to a new regular Dirichlet form on ℝ d ${\mathbb{R}^{d}}$ . More precisely, fix a regular Dirichlet form ( ℰ , ℱ ) ${(\mathcal{E,F}\kern 0.569055pt)}$ on the state space ℝ d ${\mathbb{R}^{d}}$ . Its part Dirichlet form on ℝ d ∖ { } ${\mathbb{R}^{d}\setminus\{{\mathbf{0}}\}}$ is denoted by ( ℰ 0 , ℱ ) 0 ${(\mathcal{E}^{0},\mathcal{F}{}^{0})}$ . Let ( ℰ ~ 0 , ℱ ~ ) 0 ${(\tilde{\mathcal{E}}^{0},\tilde{\mathcal{F}}{}^{0})}$ be a regular subspace of ( ℰ 0 , ℱ ) 0 ${(\mathcal{E}^{0},\mathcal{F}{}^{0})}$ . We want to find a regular subspace ( ℰ ~ , ℱ ~ ) ${(\tilde{\mathcal{E}},\tilde{\mathcal{F}}\kern 0.569055pt)}$ of ( ℰ , ℱ ) ${(\mathcal{E,F}\kern 0.569055pt)}$ such that the part Dirichlet form of ( ℰ ~ , ℱ ~ ) ${(\tilde{\mathcal{E}},\tilde{\mathcal{F}}\kern 0.569055pt)}$ on ℝ d ∖ { } ${\mathbb{R}^{d}\setminus\{{\mathbf{0}}\}}$ is exactly ( ℰ ~ 0 , ℱ ~ ) 0 ${(\tilde{\mathcal{E}}^{0},\tilde{\mathcal{F}}{}^{0})}$ . If ( ℰ ~ , ℱ ~ ) ${(\tilde{\mathcal{E}},\tilde{\mathcal{F}}\kern 0.569055pt)}$ exists, we call it a regular extension of ( ℰ ~ 0 , ℱ ~ ) 0 ${(\tilde{\mathcal{E}}^{0},\tilde{\mathcal{F}}{}^{0})}$ . We shall prove that, under a mild assumption, any rotationally invariant type regular subspace of ( ℰ 0 , ℱ ) 0 ${(\mathcal{E}^{0},\mathcal{F}{}^{0})}$ has a unique regular extension.