I would suggest you to use algorithmicx and its algcompatible variant instead of algorithmic; the former is more versatile and powerful, offers you a lot of possibilities for customization and an easy way to split algorithms, using \algstore and \algrestore; a little example:
\documentclass{article}
\usepackage[paperheight=6\baselineskip]{geometry}% just for the example
\usepackage{algorithm}
\usepackage{algcompatible}
\begin{document}
\begin{algorithm}[H]
\caption{My algo}
\begin{algorithmic}[1]
\STATE instruction 1
\STATE instruction 2
\algstore{testcont}
\end{algorithmic}
\end{algorithm}
\begin{algorithm}[H]
\caption{My algo - Part 2}
\begin{algorithmic}[1]
\algrestore{testcont}
\STATE instruction 3
\STATE instruction 4
\end{algorithmic}
\end{algorithm}
\end{document}
