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I finally found what I wanted, it is:

\newcounter{section_examples} % add a new counter
\newcounter{subsection_examples}[section_examples]
\stepcounter{section_examples} % increase the counter
\stepcounter{subsection_examples}

\subsection*{Example \arabic{section_examples}.\arabic{subsection ...

I am writing my notes of class in latex, and I would like to get the following result:

1. Algorithm (this is a section)
1.1 Newton's Method (this is a subsection of Method)
...
1.1 Example (this is a subsection of Example)
...
1.2 Example (another subsection of Example)

1.2 Lagrange Method (this ...