problem to solve a matrix

Dear R group,

I have to solve a hessian matrix 40*40, called M, in order to obtain the 
standart deviations of estimators.

When I use the function solve(M), I have the following error message: 
"Error in solve.default(M) : Lapack routine dgesv: system is exactly singular"

Do you know an alternative approach which could succeed? I have found some 
information about the function "ginv" (library MASS), has someone already 
used it in such a situation?

Thank you very much for your responses.

Eve MATHIEU.