Tropical algebra is the algebra constructed over the tropical semifield $R_{max}= (R\cup \{-\infty\},\max, +)$. We show here that every $m$-dimensional tropical module $M$ over $R_{max}$, given by a $n\times p$ matrix $A$ can be embedded into $R_{max}^n$, iff $n$ of its rows are independent. This result yields a significant improvement to the Whitney embedding for tropical torsion modules published earlier.