\documentclass[a5paper]{article}

\usepackage{algorithm,algpseudocode}
\usepackage{caption}

\begin{document}

\begin{algorithm}
  \caption{My algorithm}
  \begin{algorithmic}[1]
    \Procedure{Euclid}{$a,b$}\Comment{The g.c.d. of a and b}
      \State $r\gets a\bmod b$
      \While{$r\not=0$}\Comment{We have the answer if r is 0}
        \State $a\gets b$
        \State $b\gets r$

        \algstore{myalg}
  \end{algorithmic}
\end{algorithm}

\clearpage

\begin{algorithm}
  \ContinuedFloat
  \caption{My algorithm (continued)}
  \begin{algorithmic}
      \algrestore{myalg}

        \State $r\gets a\bmod b$
      \EndWhile\label{euclidendwhile}
      \State \textbf{return} $b$\Comment{The gcd is b}
    \EndProcedure
  \end{algorithmic}
\end{algorithm}

\end{document}
